A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011

A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011

Article Type: Communications and forum From: Kybernetes, Volume 41, Issue 7/8

In memoriam Distinguished Professor and the David C. Barrow Professor of Mathematics Dr George Adomian

I am pleased to submit my comprehensive worldwide bibliography on the Adomian decomposition method: “A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011”. It comprises over 900 titles for research papers and books by a wide variety of authors and nationalities and I consider it to be a constructive bibliography in that it features papers and books that advance the technique and extend the application of the Adomian decomposition method for solving nonlinear stochastic differential, integral, integro-differential and operator equations that model man-made device performance parameters and natural phenomena. As it has been 50 years since Dr George Adomian began his innovative research in 1961, I thought it to be appropriate to compile such a technical bibliography in memoriam. I also recalled your readers’ interest in a bibliography of his research publications after his death in 1996, and hence I thought of Kybernetes in this regard for its wide circulation among cyberneticists, systems analysts, mathematicians, scientists and engineers.

Bibliography

Abadyan, M., Beni, Y.T. and Noghrehabadi, A. (2011), “Investigation of elastic boundary condition on the pull-in instability of beam-type NEMS under van der Waals attraction”, Procedia Engineering, Vol. 10, pp. 1724-9.

Abassy, T.A. (2010), “Improved Adomian decomposition method”, Computers and Mathematics with Applications, Vol. 59 No. 1, pp. 42-54.

Abbaoui, K. (1995), “Thèse de l’Université Pierre et Marie Curie – Paris VI”, Les fondements mathématiques de la méthode décompositionnelle d’Adomian et application à la résolution de problèmes issus de la biologie et de la médicine, Université Pierre et Marie Curie – Paris VI, Paris, France, 4 October 1995.

Abbaoui, K. (1997), “Thèse d’Etat – Université de Sétif”, La méthode décompositionnelle d’Adomian et ses applications, Université de Sétif, Sétif, Algeria, 15 December 1997.

Abbaoui, K. and Cherruault, Y. (1994a), “Convergence of Adomian’s method applied to differential equations”, Computers and Mathematics with Applications, Vol. 28 No. 5, pp. 103-9.

Abbaoui, K. and Cherruault, Y. (1994b), “Convergence of Adomian’s method applied to nonlinear equations”, Mathematical and Computer Modelling, Vol. 20 No. 9, pp. 60-73.

Abbaoui, K. and Cherruault, Y. (1994c), “New ideas for solving identification and optimal control problems related to biomedical systems”, International Journal of Bio-Medical Computing, Vol. 36 No. 3, pp. 181-6.

Abbaoui, K. and Cherruault, Y. (1995), “New ideas for proving convergence of decomposition methods”, Computers and Mathematics with Applications, Vol. 29 No. 7, pp. 103-8.

Abbaoui, K. and Cherruault, Y. (1999), “The decomposition method applied to the Cauchy problem”, Kybernetes, Vol. 28 No. 1, pp. 68-74.

Abbaoui, K., Cherruault, Y. and N’Dour, M. (1995), “The decomposition method applied to differential systems”, Kybernetes, Vol. 24 No. 8, pp. 32-40.

Abbaoui, K., Cherruault, Y. and Seng, V. (1995), “Practical formulae for the calculus of multivariable Adomian polynomials”, Mathematical and Computer Modelling, Vol. 22 No. 1, pp. 89-93.

Abbaoui, K., Pujol, M.J., Cherruault, Y., Himoun, N. and Grimalt, P. (2001), “A new formulation of Adomian method: convergence result”, Kybernetes, Vol. 30 Nos 9/10, pp. 1183-91.

Abbasbandy, S. (2003), “Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method”, Applied Mathematics and Computation, Vol. 145 Nos. 2/3, pp. 887-93.

Abbasbandy, S. (2005), “Extended Newton’s method for a system of nonlinear equations by modified Adomian decomposition method”, Applied Mathematics and Computation, Vol. 170 No. 1, pp. 648-56.

Abbasbandy, S. (2007), “A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method”, Chaos, Solitons & Fractals, Vol. 31 No. 1, pp. 257-60.

Abbasbandy, S. and Darvishi, M.T. (2005a), “A numerical solution of Burgers’ equation by modified Adomian method”, Applied Mathematics and Computation, Vol. 163 No. 3, pp. 1265-72.

Abbasbandy, S. and Darvishi, M.T. (2005b), “A numerical solution of Burgers’ equation by time discretization of Adomian’s decomposition method”, Applied Mathematics and Computation, Vol. 170 No. 1, pp. 95-102.

Abdelrazec, A. (2008), “Adomian decomposition method: convergence analysis and numerical approximations”, MSc thesis (Mathematics), McMaster University, Hamilton, Ontario, Canada, November 2008, available at: www.dmpeli.mcmaster.ca/PaperBank/ThesisAhmed.pdf

Abdelrazec, A. and Pelinovsky, D. (2011), “Convergence of the Adomian decomposition method for initial-value problems”, Numerical Methods for Partial Differential Equations, Vol. 27 No. 4, pp. 749-66.

Abdelwahid, F. (2003), “A mathematical model of Adomian polynomials”, Applied Mathematics and Computation, Vol. 141 Nos 2/3, pp. 447-53.

Abdelwahid, F. and Rach, R. (2009), “On the foundation of the Adomian decomposition method”, Journal of Natural and Physical Sciences, Vol. 23 Nos 1/2, pp. 13-29.

Abdulaziz, O., Noor, N.F.M., Hashim, I. and Noorani, M.S.M. (2008), “Further accuracy tests on Adomian decomposition method for chaotic systems”, Chaos, Solitons and Fractals, Vol. 36 No. 5, pp. 1405-11.

Achouri, T. and Omrani, K. (2009), “Numerical solutions for the damped generalized regularized long-wave equation with a variable coefficient by Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14 No. 5, pp. 2025-33.

Adesanya, S.O. and Ayeni, E.R.O. (2011), “Existence and uniqueness result for couple stress bio-fluid flow model via Adomian decomposition method”, International Journal of Nonlinear Science, Vol. 12 No. 1, pp. 16-24, available at: www.internonlinearscience.org/upload/papers/20110915065005565.pdf

Adjedj, B. (1999), “Application of the decomposition method to the understanding of HIV immune dynamics”, Kybernetes, Vol. 28 No. 3, pp. 271-83.

Adomian, G., Howard Hughes Fellow, (1961), “Linear stochastic operators”, PhD dissertation (Physics), University of California at Los Angeles, Los Angeles, CA, August 1961 and July 1963; Microfilm Accession No. AAT 6402269, ProQuest/UMI (University Microfilms, Inc.), Ann Arbor, MI, February 1964.

Adomian, G. (1963a), “Linear randomly-varying systems”, in Nomura, T. (Ed.), Proceedings of the Fourth International Symposium on Space Technology and Science, Tokyo, Japan, 1962, Japan Publications Trading Co., Tokyo, p. 634.

Adomian, G. (1963b), “Linear stochastic operators”, Reviews of Modern Physics, Vol. 35 No. 1, pp. 185-207.

Adomian, G. (1964), “Stochastic Green’s functions”, in Bellman, R.E. (Ed.), Proceedings of Symposia in Applied Mathematics, Vol. XVI: Stochastic Processes in Mathematical Physics and Engineering; Proceedings of a Symposium in Applied Mathematics of the American Mathematical Society, New York, NY, USA, April 30-May 2, 1963, American Mathematical Society, Providence, RI, pp. 1-39.

Adomian, G. (1967), “Theory of random systems”, in Kožešnik, J. (Ed.), Transactions of the Fourth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Prague, Czechoslovakia, August 31-September 11, 1965, Academia, Prague and Academic Press, New York, NY, pp. 205-22.

Adomian, G. (1970), “Random operator equations in mathematical physics. I”, Journal of Mathematical Physics, Vol. 11 No. 3, pp. 1069-84.

Adomian, G. (1971a), “Linear random operator equations in mathematical physics. II”, Journal of Mathematical Physics, Vol. 12 No. 9, pp. 1944-8.

Adomian, G. (1971b), “Linear random operator equations in mathematical physics. III”, Journal of Mathematical Physics, Vol. 12 No. 9, pp. 1948-55.

Adomian, G. (1971c), “Erratum: random operator equations in mathematical physics. I, (J. Math. Phys. Vol. 11, 1069 (1970))”, Journal of Mathematical Physics, Vol. 12 No. 7, p. 1446.

Adomian, G. (1971d), “Erratum: random operator equations in mathematical physics. I, (J. Math. Phys. Vol. 11, 1069 (1970))”, Journal of Mathematical Physics, Vol. 12 No. 9, p. 2031.

Adomian, G. (1971e), “The closure approximation in the hierarchy equations”, Journal of Statistical Physics, Vol. 3 No. 2, pp. 127-33.

Adomian, G. (1972), “Addendum: linear random operator equations in mathematical physics. III, (J. Math. Phys. Vol. 12, 1948 (1971))”, Journal of Mathematical Physics, Vol. 13 No. 2, p. 272.

Adomian, G. (1975), “Obtaining first and second order statistics <y> and R_y(t₁,t₂) in stochastic differential equations for the nonlinear case”, , Vol. 10 No. 6, pp. 529-34.

Adomian, G. (1976), “Nonlinear stochastic differential equations”, Journal of Mathematical Analysis and Applications, Vol. 55 No. 2, pp. 441-52.

Adomian, G. (1977), “The solution of general linear and nonlinear stochastic systems”, in Rose, J. and Bilciu, C. (Eds.), Modern Trends in Cybernetics and Systems; in Three Volumes; Proceedings of the Third International Congress of Cybernetics and Systems, Bucharest, Romania, August 25-29, 1975; Volume II, Springer, Berlin, pp. 203-14.

Adomian, G. (1978a), “On the existence of solutions for linear and nonlinear stochastic operator equations”, Journal of Mathematical Analysis and Applications, Vol. 62 No. 2, pp. 229-35.

Adomian, G. (1978b), “New results in stochastic equations – the nonlinear case”, in Lakshmikantham, V. (Ed.), Nonlinear Equations in Abstract Spaces; Proceedings of an International Symposium on Nonlinear Equations in Abstract Spaces, University of Texas at Arlington, Arlington, TX, USA, June 8-10, 1977, Academic Press, New York, NY, pp. 3-23.

Adomian, G. (1979a), “A constructive method for linear and nonlinear stochastic partial differential equations”, in Lakshmikantham, V. (Ed.), Applied Nonlinear Analysis; Proceedings of an International Conference on Applied Nonlinear Analysis, University of Texas at Arlington, Arlington, TX, USA, April 20-22, 1978, Academic Press, New York, NY, pp. 13-23.

Adomian, G. (1979b), “Stochastic operators and dynamical systems”, in Wang, P.C.C., Schoenstadt, A.L., Russak, B.I. and Comstock, C. (Eds.), Information Linkage between Applied Mathematics and Industry; Proceedings of the First Annual Workshop on the Information Linkage between Applied Mathematics and Industry, Naval Postgraduate School, Monterey, CA, USA, February 23-25, 1978, Academic Press, New York, NY, pp. 581-96.

Adomian, G. (1980), “Stochastic systems analysis”, in Adomian, G. (Ed.), Applied Stochastic Processes; Proceedings of the Applied Stochastic Processes Conference, Center for Applied Mathematics, University of Georgia, Athens, GA, USA, May 15-19, 1978, Academic Press, New York, NY, pp. 1-17.

Adomian, G. (1981a), “On product nonlinearities in stochastic differential equations”, Applied Mathematics and Computation, Vol. 8 No. 1, pp. 79-82.

Adomian, G. (1981b), “Stochastic nonlinear modeling of fluctuations in a nuclear reactor – a new approach”, Annals of Nuclear Energy, Vol. 8 No. 7, pp. 329-30.

Adomian, G. (1982a), “Stochastic model for colored noise”, Journal of Mathematical Analysis and Applications, Vol. 88 No. 2, pp. 607-9.

Adomian, G. (1982b), “On Green’s function in higher order stochastic differential equations”, Journal of Mathematical Analysis and Applications, Vol. 88 No. 2, pp. 604-6.

Adomian, G. (1982c), “Solution of nonlinear stochastic physical problems”, Rendiconti del Seminario Matematico Università e Politecnico di Torino, Vol. 40, No. Special, pp. 7-22.

Adomian, G. (1982d), “Stabilization of a stochastic nonlinear economy”, Journal of Mathematical Analysis and Applications, Vol. 88 No. 1, pp. 306-17.

Adomian, G. (1982e), “Application of stochastic differential equations to economics”, in Stochastic Differential Equations; Proceedings of the “5-Tage-Kurs” of the USP Mathematisierung at Bielefeld University, Bielefeld, Germany, October 12-16, 1981; Materialien des Universitätsschwerpunktes Mathematisierung der Einzelwissenschaften, Vol. 38, Universität Bielefeld, Bielefeld, Germany.

Adomian, G. (1983a), “Approximate calculation of Green’s functions”, Journal of Approximation Theory, Vol. 37 No. 2, pp. 119-24.

Adomian, G. (1983b), “Partial differential equations with integral boundary conditions”, Computers and Mathematics with Applications, Vol. 9 No. 3, pp. 443-5.

Adomian, G. (1983c), Stochastic Systems, Academic Press, New York, NY.

Adomian, G. (1984a), “A new approach to nonlinear partial differential equations”, Journal of Mathematical Analysis and Applications, Vol. 102 No. 2, pp. 420-34.

Adomian, G. (1984b), “Convergent series solution of nonlinear equations”, Journal of Computational and Applied Mathematics, Vol. 11 No. 2, pp. 225-30.

Adomian, G. (1984c), “On the convergence region for decomposition solutions”, Journal of Computational and Applied Mathematics, Vol. 11 No. 3, pp. 379-80.

Adomian, G. (1985a), “Discretization, decomposition and supercomputers”, Journal of Mathematical Analysis and Applications, Vol. 112 No. 2, pp. 487-96.

Adomian, G. (1985b), “New approaches to solution of national economy models and business cycles”, Kybernetes, Vol. 14 No. 4, pp. 221-3.

Adomian, G. (1985c), “Nonlinear stochastic dynamical systems in physical problems”, Journal of Mathematical Analysis and Applications, Vol. 111 No. 1, pp. 105-13.

Adomian, G. (1985d), “Random eigenvalue equations”, Journal of Mathematical Analysis and Applications, Vol. 111 No. 2, pp. 427-32.

Adomian, G. (1986a), “A new approach to the heat equation – an application of the decomposition method”, Journal of Mathematical Analysis and Applications, Vol. 113 No. 1, pp. 202-9.

Adomian, G. (1986b), “Application of the decomposition method to the Navier-Stokes equations”, Journal of Mathematical Analysis and Applications, Vol. 119 Nos 1/2, pp. 340-60.

Adomian, G. (1986c), “Inversion of matrices”, Mathematics and Computers in Simulation, Vol. 28 No. 2, pp. 151-3.

Adomian, G. (1986d), “Nonlinear equations with mixed derivatives”, Journal of Mathematical Analysis and Applications, Vol. 120 No. 2, pp. 734-6.

Adomian, G. (1986e), “Nonlinear hyperbolic initial value problem”, Journal of Mathematical Analysis and Applications, Vol. 120 No. 2, pp. 730-3.

Adomian, G. (1986f), “Solution of the Navier-Stokes equation – I”, Computers and Mathematics with Applications, Vol. 12 No. 11, Pt. A, pp. 1119-24.

Adomian, G. (1986g), “Solution of Lanchester equation models for combat”, Journal of Mathematical Analysis and Applications, Vol. 114 No. 1, pp. 176-7.

Adomian, G. (1986h), “Solution of algebraic equations”, Mathematics and Computers in Simulation, Vol. 28 No. 2, pp. 155-7.

Adomian, G. (1986i), “Stochastic water reservoir modeling”, Journal of Mathematical Analysis and Applications, Vol. 115 No. 1, pp. 233-4.

Adomian, G. (1986j), “Systems of nonlinear partial differential equations”, Journal of Mathematical Analysis and Applications, Vol. 115 No. 1, pp. 235-8.

Adomian, G. (1986k), “State-delayed matrix differential-difference equations”, Journal of Mathematical Analysis and Applications, Vol. 114 No. 2, pp. 426-8.

Adomian, G. (1986l), “The decomposition method for nonlinear dynamical systems”, Journal of Mathematical Analysis and Applications, Vol. 120 No. 1, pp. 370-83.

Adomian, G. (1986m), “Decomposition solution for Duffing and van der Pol oscillators”, International Journal of Mathematics and Mathematical Sciences, Vol. 9 No. 4, pp. 731-2, doi:10.1155/S016117128600087X.

Adomian, G. (1986n), Nonlinear Stochastic Operator Equations, Academic Press, Orlando, FL.

Adomian, G. (1987a), “Vibration in offshore structures: an analysis for the general nonlinear stochastic case – Part I”, Mathematics and Computers in Simulation, Vol. 29 No. 2, pp. 119-22.

Adomian, G. (1987b), “Vibration in offshore structures – Part II”, Mathematics and Computers in Simulation, Vol. 29 No. 5, pp. 351-6.

Adomian, G. (1987c), “Wave propagation in nonlinear media”, Applied Mathematics and Computation, Vol. 24 No. 4, pp. 311-32.

Adomian, G. (1987d), “Semilinear wave equations”, Computers and Mathematics with Applications, Vol. 14 No. 6, pp. 497-9.

Adomian, G. (1987e), “Nonlinear oscillations in physical systems”, Mathematics and Computers in Simulation, Vol. 29 Nos. 3/4, pp. 275-84.

Adomian, G. (1987f), “A general approach to solution of partial differential equation systems”, Computers and Mathematics with Applications, Vol. 13 Nos. 9/11, pp. 741-7.

Adomian, G. (1987g), “A new approach to the Efinger model for a nonlinear quantum theory for gravitating particles”, Foundations of Physics, Vol. 17 No. 4, pp. 419-23.

Adomian, G. (1987h), “An investigation of the asymptotic decomposition method for nonlinear equations in physics”, Applied Mathematics and Computation, Vol. 24 No. 1, pp. 1-17.

Adomian, G. (1987i), “Modeling and solving physical problems”, Mathematical Modelling, Vol. 8, pp. 57-60.

Adomian, G. (1987j), “Modification of the decomposition approach to the heat equation”, Journal of Mathematical Analysis and Applications, Vol. 124 No. 1, pp. 290-1.

Adomian, G. (1987k), “Analytical solutions for ordinary and partial differential equations”, in Knowles, I.W. and Saito, Y. (Eds.), Differential Equations and Mathematical Physics; Proceedings of an International Conference, Birmingham, Alabama, USA, March 3-8, 1986, Lecture Notes in Mathematics (LNM), Vol. 1285, Springer, Berlin, pp. 1-15.

(1987l),

Adomian, G. (1988a), “A general approach for complex systems”, Kybernetes, Vol. 17 No. 1, pp. 49-59.

Adomian, G. (1988b), “A new approach to Burger’s equation”, Physica D: Nonlinear Phenomena, Vol. 31 No. 1, pp. 65-9.

Adomian, G. (1988c), “A review of the decomposition method in applied mathematics”, Journal of Mathematical Analysis and Applications, Vol. 135 No. 2, pp. 501-44.

Adomian, G. (1988d), “An adaptation of the decomposition method for asymptotic solutions”, Mathematics and Computers in Simulation, Vol. 30 No. 4, pp. 325-9.

Adomian, G. (1988e), “Analysis of model equations of gas dynamics”, AIAA Journal, Vol. 26 No. 2, pp. 242-4.

Adomian, G. (1988f), “Analytic solutions for nonlinear equations”, Applied Mathematics and Computation, Vol. 26 No. 1, pp. 77-88.

Adomian, G. (1988g), “Application of decomposition to convection-diffusion equations”, Applied Mathematics Letters, Vol. 1 No. 1, pp. 7-9.

Adomian, G. (1988h), “Corrigenda and comment on ‘a general approach to solution of partial differential equation systems’”, Computers and Mathematics with Applications, Vol. 15 Nos. 6/8, p. 711.

Adomian, G. (1988i), “Elliptic equations and decomposition”, Computers and Mathematics with Applications, Vol. 15 No. 1, pp. 65-7.

Adomian, G. (1988j), “New approach to the analysis and control of large space structures”, AIAA Journal, Vol. 26 No. 3, pp. 377-80.

Adomian, G. (1988k), “Propagation in dissipative or dispersive media”, Journal of Computational and Applied Mathematics, Vol. 23 No. 3, pp. 395-6.

Adomian, G. (1988l), “Solving the nonlinear equations of physics”, Computers and Mathematics with Applications, Vol. 16 Nos 10/11, pp. 903-14.

Adomian, G. (1989a), “Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations”, International Journal of Mathematics and Mathematical Sciences, Vol. 12 No. 1, pp. 137-44.

Adomian, G. (1989b), “Comments on a ‘counterexample’ to decomposition”, Journal of Computational and Applied Mathematics, Vol. 26 No. 3, pp. 375-6.

Adomian, G. (1989c), “Speculations on possible directions and applications for the decomposition method”, in Blaquiére, A. (Ed.), Modeling and Control of Systems in Engineering, Quantum Mechanics, Economics and Biosciences; Proceedings of the Third Bellman Continuum Workshop, Sophia Antipolis, France, June 13-14, 1988, Lecture Notes in Control and Information Sciences (LNCIS), Vol. 121, Springer, Berlin, pp. 479-95.

Adomian, G. (1989d), Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers, Dordrecht.

Adomian, G. (1990), “Decomposition solution of nonlinear hyperbolic equations”, Mathematical and Computer Modelling, Vol. 14, pp. 80-2.

Adomian, G. (1991a), “A review of the decomposition method and some recent results for nonlinear equations”, Computers and Mathematics with Applications, Vol. 21 No. 5, pp. 101-27.

Adomian, G. (1991b), “An analytical solution of the stochastic Navier-Stokes system”, Foundations of Physics, Vol. 21 No. 7, pp. 831-43.

Adomian, G. (1991c), “Solving frontier problems modelled by nonlinear partial differential equations”, Computers and Mathematics with Applications, Vol. 22 No. 8, pp. 91-4.

Adomian, G. (1991d), “The sine-Gordon, Klein-Gordon and Korteweg-de Vries equations”, Computers and Mathematics with Applications, Vol. 21 No. 5, pp. 133-6.

Adomian, G. (1991e), “Errata to ‘a review of the decomposition method and some recent results for nonlinear equations’: (Computers Math. Applic., Vol. 21 No. 5, 1991, pp. 101-127)”, Computers and Mathematics with Applications, Vol. 22 No. 8, p. 95.

Adomian, G. (1993a) “A class of nonlinear relativistic partial differential equations in elementary particle theory”, Foundations of Physics Letters, Vol. 6 No. 6, pp. 603-5.

Adomian, G. (1993b) “The N-body problem”, Foundations of Physics Letters, Vol. 6 No. 6, pp. 597-602.

Adomian, G. (1994a) “Solution of nonlinear evolution equations”, Mathematical and Computer Modelling, Vol. 20 No. 12, pp. 1-2.

Adomian, G. (1994b) “Solution of physical problems by decomposition”, Computers and Mathematics with Applications, Vol. 27 Nos 9/10, pp. 145-54.

Adomian, G. (1994c) “The origin of chaos”, Foundations of Physics Letters, Vol. 7 No. 6, pp. 585-9.

Adomian, G. (1994d), Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Dordrecht.

Adomian, G. (1995a), “Solving the mathematical models of neurosciences and medicine”, Mathematics and Computers in Simulation, Vol. 40 Nos 1/2, pp. 107-14.

Adomian, G. (1995b), “A new approach to solution of the Maxwell equations”, Foundations of Physics Letters, Vol. 8 No. 6, pp. 583-7.

Adomian, G. (1995c), “Analytical solution of Navier-Stokes flow of a viscous compressible fluid”, Foundations of Physics Letters, Vol. 8 No. 4, pp. 389-400.

Adomian, G. (1995d), “Delayed nonlinear dynamical systems”, Mathematical and Computer Modelling, Vol. 22 No. 3, pp. 77-9.

Adomian, G. (1995e), “Fisher-Kolmogorov equation”, Applied Mathematics Letters, Vol. 8 No. 2, pp. 51-2.

Adomian, G. (1995f), “On integral, differential and integro-differential equations, perturbation and averaging methods”, Kybernetes, Vol. 24 No. 7, pp. 52-60.

Adomian, G. (1995g), “Random Volterra integral equations”, Mathematical and Computer Modelling, Vol. 22 No. 8, pp. 101-2.

Adomian, G. (1995h), “Stochastic Burgers’ equation”, Mathematical and Computer Modelling, Vol. 22 No. 8, pp. 103-5.

Adomian, G. (1995i), “The diffusion-Brusselator equation”, Computers and Mathematics with Applications, Vol. 29 No. 5, pp. 1-3.

Adomian, G. (1995j), “The Nikolaevskiy model for nonlinear seismic waves”, Mathematical and Computer Modelling, Vol. 22 No. 3, pp. 81-2.

Adomian, G. (1995k), “The generalized Kolmogorov-Petrovskii-Piskunov equation”, Foundations of Physics Letters, Vol. 8 No. 1, pp. 99-101.

Adomian, G. (1996a), “The Kadomtsev-Petviashvili equation”, Applied Mathematics and Computation, Vol. 76 No. 1, pp. 95-7.

Adomian, G. (1996b), “A non-perturbative solution of N-body dynamics”, Foundations of Physics Letters, Vol. 9 No. 3, pp. 301-8.

Adomian, G. (1996c), “Coupled Maxwell equations for electromagnetic scattering”, Applied Mathematics and Computation, Vol. 77 Nos 2/3, pp. 133-5.

Adomian, G. (1996d), “Nonlinear Klein-Gordon equation”, Applied Mathematics Letters, Vol. 9 No. 3, pp. 9-10.

Adomian, G. (1996e), “Nonlinear random vibration”, Applied Mathematics and Computation, Vol. 77 Nos 2/3, pp. 109-12.

Adomian, G. (1996f), “Solution of coupled nonlinear partial differential equations by decomposition”, Computers and Mathematics with Applications, Vol. 31 No. 6, pp. 117-20.

Adomian, G. (1996g), “The Burridge-Knopoff model”, Applied Mathematics and Computation, Vol. 77 Nos 2/3, pp. 131-2.

Adomian, G. (1996h), “The dissipative sine-Gordon equation”, Foundations of Physics Letters, Vol. 9 No. 4, pp. 407-10.

Adomian, G. (1996i), “The fifth-order Korteweg-de Vries equation”, International Journal of Mathematics and Mathematical Sciences, Vol. 19 No. 2, p. 415, doi:10.1155/S0161171296000592.

Adomian, G. (1997a), “Explicit solutions of nonlinear partial differential equations”, Applied Mathematics and Computation, Vol. 88 Nos. 2/3, pp. 117-26.

Adomian, G. (1997b), “Non-perturbative solution of the Klein-Gordon-Zakharov equation”, Applied Mathematics and Computation, Vol. 81 No. 1, pp. 89-92.

Adomian, G. (1997c), “On KdV type equations”, Applied Mathematics and Computation, Vol. 88 Nos. 2/3, pp. 131-5.

Adomian, G. (1997d), “On the dynamics of a reaction-diffusion system”, Applied Mathematics and Computation, Vol. 81 No. 1, pp. 93-5.

Adomian, G. (1997e), “Optical propagation in random media”, Applied Mathematics and Computation, Vol. 88 Nos. 2/3, pp. 127-9.

Adomian, G. (1998a), “Analytic solution of nonlinear integral equations of Hammerstein type”, Applied Mathematics Letters, Vol. 11 No. 3, pp. 127-30.

Adomian, G. (1998b), “Nonlinear dissipative wave equations”, Applied Mathematics Letters, Vol. 11 No. 3, pp. 125-6.

Adomian, G. (1998c), “Solution of the Thomas-Fermi equation”, Applied Mathematics Letters, Vol. 11, No. 3, pp. 131-3.

Adomian, G. (1998d), “Solutions of nonlinear P.D.E.”, Applied Mathematics Letters, Vol. 11 No. 3, pp. 121-3.

Adomian, G. and Adomian, G.E. (1984), “A global method for solution of complex systems”, Mathematical Modelling, Vol. 5 No. 4, pp. 251-63.

Adomian, G. and Adomian, G.E. (1985), “Cellular systems and aging models”, Computers and Mathematics with Applications, Vol. 11 Nos. 1/3, pp. 283-91.

Adomian, G. and Adomian, G.E. (1986), “Solution of the Marchuk model of infectious disease and immune response”, Mathematical Modelling, Vol. 7 Nos 5/8, pp. 803-7.

Adomian, G., Adomian, G.E. and Bellman, R.E. (1984), “Biological system interactions”, Proceedings of the National Academy of Sciences of the United States of America, Vol. 81 No. 9, pp. 2938-40.

Adomian, G. and Bellman, R.E. (1982), “On the Itô equation”, Journal of Mathematical Analysis and Applications, Vol. 86 No. 2, pp. 476-8.

Adomian, G. and Bellomo, N. (1986), “On the Tricomi problem”, Computers and Mathematics with Applications, Vol. 12 Nos 4/5, Pt. A, pp. 557-63.

Adomian, G., Bellomo, N. and Riganti, R. (1983), “Semilinear stochastic systems: analysis with the method of the stochastic Green’s function and application in mechanics”, Journal of Mathematical Analysis and Applications, Vol. 96 No. 2, pp. 330-40.

Adomian, G., Bigi, D. and Riganti, R. (1985), “On the solutions of stochastic initial-value problems in continuum mechanics”, Journal of Mathematical Analysis and Applications, Vol. 110 No. 2, pp. 442-62.

Adomian, G., Cherruault, Y. and Abbaoui, K. (1996), “A nonperturbative analytical solution of immune response with time-delays and possible generalization”, Mathematical and Computer Modelling, Vol. 24 No. 10, pp. 89-96.

Adomian, G. and Efinger, H.J. (1994), “Analytic solutions for time-dependent Schrödinger equations with linear or nonlinear Hamiltonians”, Foundations of Physics Letters, Vol. 7 No. 5, pp. 489-91.

Adomian, G. and Elrod, M. (1981), “Generation of a stochastic process with desired first- and second-order statistics”, Kybernetes, Vol. 10 No. 1, pp. 25-30.

Adomian, G., Elrod, M. and Rach, R. (1989), “A new approach to boundary value equations and application to a generalization of Airy’s equation”, Journal of Mathematical Analysis and Applications, Vol. 140 No. 2, pp. 554-68.

Adomian, G. and Lynch, T. (1977), “Stochastic differential operator equations with random initial conditions”, Journal of Mathematical Analysis and Applications, Vol. 61 No. 1, pp. 216-26.

Adomian, G. and Malakian, K. (1979), “Closure approximation error in the mean solution of stochastic differential equations by the hierarchy method”, Journal of Statistical Physics, Vol. 21 No. 2, pp. 181-9.

Adomian, G. and Malakian, K. (1980a), “Operator-theoretic solution of stochastic systems”, Journal of Mathematical Analysis and Applications, Vol. 76 No. 1, pp. 183-201.

Adomian, G. and Malakian, K. (1980b), “Inversion of stochastic partial differential operators – the linear case”, Journal of Mathematical Analysis and Applications, Vol. 77 No. 2, pp. 505-12.

Adomian, G. and Malakian, K. (1980c), “Self-correcting approximate solution by the iterative method for linear and nonlinear stochastic differential equations”, Journal of Mathematical Analysis and Applications, Vol. 76 No. 2, pp. 309-27.

Adomian, G. and Malakian, K. (1980d), “Stochastic analysis”, Mathematical Modelling, Vol. 1 No. 3, pp. 211-35.

Adomian, G. and Malakian, K. (1981), “A comparison of the iterative method and Picard’s successive approximations for deterministic and stochastic differential equations, Applied Mathematics and Computation, Vol. 8 No. 3, pp. 187-204.

Adomian, G. and Malakian, K. (1982), “Existence and uniqueness of statistical measures for solution processes for linear-stochastic differential equations”, Journal of Mathematical Analysis and Applications, Vol. 89 No. 1, pp. 186-92.

Adomian, G. and Malakian, K. (1986), “Existence of the inverse of a linear stochastic operator”, Journal of Mathematical Analysis and Applications, Vol. 114 No. 1, pp. 55-6.

Adomian, G. and Meyers, R.E. (1993), “Nonlinear transport in moving fluids”, Applied Mathematics Letters, Vol. 6 No. 5, pp. 35-8.

Adomian, G. and Meyers, R.E. (1995a), “Generalized nonlinear Schrödinger equation with time-dependent dissipation”, Applied Mathematics Letters, Vol. 8 No. 6, pp. 7-8.

Adomian, G. and Meyers, R.E. (1995b), “Isentropic flow of an inviscid gas”, Applied Mathematics Letters, Vol. 8 No. 1, pp. 43-6.

Adomian, G. and Meyers, R.E. (1995c), “The Ginzburg-Landau equation”, Computers and Mathematics with Applications, Vol. 29 No. 3, pp. 3-4.

Adomian, G., Pandolfi, M. and Rach, R. (1988), “An application of the decomposition method to the matrix Riccati equation in a neutron transport process”, Journal of Mathematical Analysis and Applications, Vol. 136 No. 2, pp. 557-67.

Adomian, G. and Rach, R. (1983a), “Inversion of nonlinear stochastic operators”, Journal of Mathematical Analysis and Applications, Vol. 91 No. 1, pp. 39-46.

Adomian, G. and Rach, R. (1983b), “Anharmonic oscillator systems”, Journal of Mathematical Analysis and Applications, Vol. 91 No. 1, pp. 229-36.

Adomian, G. and Rach, R. (1983c), “A nonlinear differential delay equation”, Journal of Mathematical Analysis and Applications, Vol. 91 No. 2, pp. 301-4.

Adomian, G. and Rach, R. (1983d), “Nonlinear stochastic differential delay equations”, Journal of Mathematical Analysis and Applications, Vol. 91 No. 1, pp. 94-101.

Adomian, G. and Rach, R. (1984a), “Light scattering in crystals”, Journal of Applied Physics, Vol. 56 No. 9, pp. 2592-4.

Adomian, G. and Rach, R. (1984b), “On nonzero initial conditions in stochastic differential equations”, Journal of Mathematical Analysis and Applications, Vol. 102 No. 2, pp. 363-4.

Adomian, G. and Rach, R. (1985a), “Algebraic equations with exponential terms”, Journal of Mathematical Analysis and Applications, Vol. 112 No. 1, pp. 136-40.

Adomian, G. and Rach, R. (1985b), “Application of the decomposition method to inversion of matrices”, Journal of Mathematical Analysis and Applications, Vol. 108 No. 2, pp. 409-21.

Adomian, G. and Rach, R. (1985c) “An algorithm for transient dynamic analysis”, Transactions of the Society for Computer Simulation, Vol. 2 No. 4, pp. 321-7.

Adomian, G. and Rach, R. (1985d), “Coupled differential equations and coupled boundary conditions”, Journal of Mathematical Analysis and Applications, Vol. 112 No. 1, pp. 129-35.

Adomian, G. and Rach, R. (1985e), “Nonlinear differential equations with negative power nonlinearities”, Journal of Mathematical Analysis and Applications, Vol. 112 No. 2, pp. 497-501.

Adomian, G. and Rach, R. (1985f), “Nonlinear plasma response”, Journal of Mathematical Analysis and Applications, Vol. 111 No. 1, pp. 114-8.

Adomian, G. and Rach, R. (1985g), “On the solution of algebraic equations by the decomposition method”, Journal of Mathematical Analysis and Applications, Vol. 105 No. 1, pp. 141-66.

Adomian, G. and Rach, R. (1985h), “Polynomial nonlinearities in differential equations”, Journal of Mathematical Analysis and Applications, Vol. 109 No. 1, pp. 90-5.

Adomian, G. and Rach, R. (1986a), “On the solution of nonlinear differential equations with convolution product nonlinearities”, Journal of Mathematical Analysis and Applications, Vol. 114 No. 1, pp. 171-5.

Adomian, G. and Rach, R. (1986b), “A coupled nonlinear system”, Journal of Mathematical Analysis and Applications, Vol. 113 No. 2, pp. 510-3.

Adomian, G. and Rach, R. (1986c), “A new computational approach for inversion of very large matrices”, Mathematical Modelling, Vol. 7 Nos. 2/3, pp. 113-41.

Adomian, G. and Rach, R. (1986d), “Algebraic computation and the decomposition method”, Kybernetes, Vol. 15 No. 1, pp. 33-7.

Adomian, G. and Rach, R. (1986e), “On composite nonlinearities and the decomposition method”, Journal of Mathematical Analysis and Applications, Vol. 113 No. 2, pp. 504-9.

Adomian, G. and Rach, R. (1986f), “On linear and nonlinear integro-differential equations”, Journal of Mathematical Analysis and Applications, Vol. 113 No. 1, pp. 199-201.

Adomian, G. and Rach, R. (1986g), “Solving nonlinear differential equations with decimal power nonlinearities”, Journal of Mathematical Analysis and Applications, Vol. 114 No. 2, pp. 423-5.

Adomian, G. and Rach, R. (1986h), “The noisy convergence phenomena in decomposition method solutions”, Journal of Computational and Applied Mathematics, Vol. 15 No. 3, pp. 379-81.

Adomian, G. and Rach, R. (1987), “Explicit solutions for differential equations”, Applied Mathematics and Computation, Vol. 23 No. 1, pp. 49-59.

Adomian, G. and Rach, R. (1988), “Evaluation of integrals by decomposition”, Journal of Computational and Applied Mathematics, Vol. 23 No. 1, pp. 99-101.

Adomian, G. and Rach, R. (1989), “Analytic parametrization and the decomposition method”, Applied Mathematics Letters, Vol. 2 No. 4, pp. 311-3.

Adomian, G. and Rach, R., (1990a) “Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations”, Computers and Mathematics with Applications, Vol. 19 No. 12, pp. 9-12.

Adomian, G. and Rach, R. (1990b), “Purely nonlinear differential equations”, Computers and Mathematics with Applications, Vol. 20 No. 1, pp. 1-3.

Adomian, G. and Rach, R. (1991a), “Linear and nonlinear Schrödinger equations”, Foundations of Physics, Vol. 21 No. 8, pp. 983-91.

Adomian, G. and Rach, R. (1991b), “Solution of nonlinear ordinary and partial differential equations of physics”, Journal of Mathematical and Physical Sciences, Vol. 25 Nos 5/6, pp. 703-18.

Adomian, G. and Rach, R. (1991c), “Transformation of series”, Applied Mathematics Letters, Vol. 4 No. 4, pp. 69-71.

Adomian, G. and Rach, R. (1992a), “A further consideration of partial solutions in the decomposition method”, Computers and Mathematics with Applications, Vol. 23 No. 1, pp. 51-64.

Adomian, G. and Rach, R. (1992b), “An approach to steady-state solutions”, Applied Mathematics Letters, Vol. 5 No. 5, pp. 39-40.

Adomian, G. and Rach, R. (1992c), “Generalization of Adomian polynomials to functions of several variables”, Computers and Mathematics with Applications, Vol. 24 Nos. 5/6, pp. 11-24.

Adomian, G. and Rach, R. (1992d), “Inhomogeneous nonlinear partial differential equations with variable coefficients”, Applied Mathematics Letters, Vol. 5 No. 2, pp. 11-2.

Adomian, G. and Rach, R. (1992e), “Modified decomposition solution of nonlinear partial differential equations”, Applied Mathematics Letters, Vol. 5 No. 6, pp. 29-30.

Adomian, G. and Rach, R. (1992f), “Noise terms in decomposition solution series”, Computers and Mathematics with Applications, Vol. 24 No. 11, pp. 61-4.

Adomian, G. and Rach, R. (1992g), “Nonlinear transformation of series – Part II”, Computers and Mathematics with Applications, Vol. 23 No. 10, pp. 79-83.

Adomian, G. and Rach, R. (1993a) “A new algorithm for matching boundary conditions in decomposition solutions”, Applied Mathematics and Computation, Vol. 58 No. 1, pp. 61-8.

Adomian, G. and Rach, R. (1993b) “Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition”, Journal of Mathematical Analysis and Applications, Vol. 174 No. 1, pp. 118-37.

Adomian, G. and Rach, R. (1993c) “Solution of nonlinear partial differential equations in one, two, three and four dimensions”, World Scientific Series in Applicable Analysis, Vol. 2, pp. 1-13.

Adomian, G. and Rach, R. (1994a), “A new algorithm for solution of the harmonic oscillator by decomposition”, Applied Mathematics Letters, Vol. 7 No. 1, pp. 53-6.

Adomian, G. and Rach, R. (1994b), “Modified decomposition solution of linear and nonlinear boundary-value problems”, Nonlinear Analysis, Theory, Methods and Applications, Vol. 23 No. 5, pp. 615-9.

Adomian, G. and Rach, R. (1995), “Kuramoto-Sivashinsky equation”, Journal of Applied Science and Computations, Vol. 1 No. 3, pp. 476-80.

Adomian, G. and Rach, R. (1996), “Modified Adomian polynomials”, Mathematical and Computer Modelling, Vol. 24 No. 11, pp. 39-46.

Adomian, G., Rach, R. and Elrod, M. (1988), “The decomposition method applied to stiff systems”, Mathematics and Computers in Simulation, Vol. 30 No. 3, pp. 271-6.

Adomian, G., Rach, R. and Elrod, M. (1989), “On the solution of partial differential equations with specified boundary conditions”, Journal of Mathematical Analysis and Applications, Vol. 140 No. 2, pp. 569-81.

Adomian, G., Rach, R. and Meyers, R.E. (1991a), “An efficient methodology for the physical sciences”, Kybernetes, Vol. 20 No. 7, pp. 24-34.

Adomian, G., Rach, R. and Meyers, R.E. (1991b), “Numerical algorithms and decomposition”, Computers and Mathematics with Applications, Vol. 22 No. 8, pp. 57-61.

Adomian, G., Rach, R. and Meyers, R.E. (1994), “Solution of generic nonlinear oscillators”, Applied Mathematics and Computation, Vol. 64 Nos 2/3, pp. 167-70.

Adomian, G., Rach, R. and Meyers, R.E. (1997), “Numerical integration, analytic continuation and decomposition”, Applied Mathematics and Computation, Vol. 88 Nos 2/3, pp. 95-116.

Adomian, G., Rach, R. and Sarafyan, D. (1985), “On the solution of equations containing radicals by the decomposition method”, Journal of Mathematical Analysis and Applications, Vol. 111 No. 2, pp. 423-6.

Adomian, G., Rach, R. and Shawagfeh, N.T. (1995), “On the analytic solution of the Lane-Emden equation”, Foundations of Physics Letters, Vol. 8 No. 2, pp. 161-81.

Adomian, G. and Sarafyan, D. (1981), “Numerical solution of differential equations in the deterministic limit of stochastic theory”, Applied Mathematics and Computation, Vol. 8 No. 2, pp. 111-9.

Adomian, G. and Serrano, S.E. (1998), “Stochastic contaminant transport equation in porous media”, Applied Mathematics Letters, Vol. 11 No. 1, pp. 53-5.

Adomian, G. and Sibul, L.H. (1971), “Propagation in stochastic media”, Proceedings of the 1971 Antennas and Propagation Society International Symposium, Vol. 9, IEEE, pp. 163-5, doi:10.1109/APS.1971.1150900.

Adomian, G. and Sibul, L.H. (1977), “Stochastic Green’s formula and application to stochastic differential equations”, Journal of Mathematical Analysis and Applications, Vol. 60 No. 3, pp. 743-6.

Adomian, G. and Sibul, L.H. (1981a), “On the control of stochastic systems”, Journal of Mathematical Analysis and Applications, Vol. 83 No. 2, pp. 611-21.

Adomian, G. and Sibul, L.H. (1981b), “Symmetrized solutions for nonlinear stochastic differential equations”, International Journal of Mathematics and Mathematical Sciences, Vol. 4 No. 3, pp. 529-42, doi:10.1155/S0161171281000380.

Adomian, G., Sibul, L.H. and Rach, R. (1983), “Coupled nonlinear stochastic differential equations”, Journal of Mathematical Analysis and Applications, Vol. 92 No. 2, pp. 427-34.

Adomian, G. and Vasudevan, R. (1984), “A stochastic approach to inverse scattering in geophysical layers”, Mathematical Modelling, Vol. 5 No. 5, pp. 339-42.

Adomian, G. and Witten, M. (1994), “Computation of solutions to the generalized Michaelis-Menton equation”, Applied Mathematics Letters, Vol. 7 No. 4, pp. 45-8.

Afrouzi, G.A. and Khademloo, S. (2006), “On Adomian decomposition method for solving reaction diffusion equation”, International Journal of Nonlinear Science, Vol. 2 No. 1, pp. 11-5, available at: www.worldacademicunion.com/journal/1749-3889-3897IJNS/IJNSVol2No1Paper2.pdf

Alabdullatif, M., Abdusalam, H.A. and Fahmy, E.S. (2007), “Adomian decomposition method for nonlinear reaction diffusion system of Lotka-Volterra type”, International Mathematical Forum, Vol. 2 No. 2, pp. 87-96, available at: www.m-hikari.com/imf-password2007/1-4-2007/abdusalamIMF1-4-2007.pdf

Al-Bayati, A.Y., Al-Sawoor, A.J. and Samarji, M.A. (2009), “A multistage Adomian decomposition method for solving the autonomous van der Pol system”, Australian Journal of Basic and Applied Sciences, Vol. 3 No. 4, pp. 4397-407.

Al-Dosary, K.I., Al-Jubouri, N.K. and Abdullah, H.K. (2008), “On the solution of Abel differential equation by Adomian decomposition method”, Applied Mathematical Sciences, Vol. 2, No. 43, 2105-18.

Alharbi, A. and Fahmy, E.S. (2010), “ADM-Padé solutions for generalized Burgers and Burgers-Huxley systems with two coupled equations”, Journal of Computational and Applied Mathematics, Vol. 233 No. 8, pp. 2071-80.

Al-Hayani, W. (2011), “Adomian decomposition method with Green’s function for sixth-order boundary value problems”, Computers and Mathematics with Applications, Vol. 61 No. 6, pp. 1567-75.

Al-Hayani, W. and Casasús, L. (2005a), “Approximate analytical solution of fourth order boundary value problems”, Numerical Algorithms, Vol. 40 No. 1, pp. 67-78.

Al-Hayani, W. and Casasús, L. (2005b), “The Adomian decomposition method in turning point problems”, Journal of Computational and Applied Mathematics, Vol. 177 No. 1, pp. 187-203.

Al-Hayani, W. and Casasús, L. (2006), “On the applicability of the Adomian method to initial value problems with discontinuities”, Applied Mathematics Letters, Vol. 19 No. 1, pp. 22-31.

Al-Humedi, H.O. and Ali, A.H. (2008), “Application of Adomian decomposition method to solve Fisher’s equation”, Journal of Basrah Researches (Sciences), Vol. 35, pp. 23-32.

Al-Humedi, H.O. and Al-Qatrany, F.L.H. (2010), “Modified algorithm to compute Adomian’s polynomials for solving non-linear systems of partial differential equations”, International Journal of Contemporary Mathematical Sciences, Vol. 5 No. 51, pp. 2505-21, available at: www.m-hikari.com/ijcms-2010/49-52-2010/odaIJCMS49-52-2010.pdf

Ali, A.H. and Al-Saif, A.S.J. (2008), “Adomian decomposition method for solving some models of nonlinear partial differential equations”, Basrah Journal of Science (A), Vol. 26 No. 1, pp. 1-11.

Alizadeh, E., Sedighi, K., Farhadi, M. and Ebrahimi-Kebria, H.R. (2009), “Analytical approximate solution of the cooling problem by Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14 No. 2, pp. 462-72.

Al-Khaled, K. and Allan, F. (2004), “Construction of solutions for the shallow water equations by the decomposition method”, Mathematics and Computers in Simulation, Vol. 66 No. 6, pp. 479-86.

Al-Khaled, K., Kaya, D. and Noor, M.A. (2004), “Numerical comparison of methods for solving parabolic equations”, Applied Mathematics and Computation, Vol. 157 No. 3, pp. 735-43.

Al-Khawaja, U. and Al-Khaled, K. (2007), “Error control in Adomian’s decomposition method applied to the time-dependent Gross-Pitaevskii equation”, International Journal of Computer Mathematics, Vol. 84 No. 1, pp. 81-7.

Al-Kurdi, A. and Mulhem, S. (2011), “Solution of twelfth order boundary value problems using Adomian decomposition method”, Journal of Applied Sciences Research, Vol. 7 No. 6, pp. 922-34, available at: www.aensionline.com/jasr/jasr/2011/922-934.pdf

Al-Mazmumy, M.A., “Adomian decomposition method for solving Goursat’s problems” (2011), SR (Scientific Research) Applied Mathematics, Vol. 2 No. 8, pp. 975-80, doi:10.4236/am.2011.28134

Aly, E.H., Ebaid, A. and Rach, R. (2012), “Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions”, Computers and Mathematics with Applications, Vol. 63 No. 6, pp. 1056-65.

Amani, A.R. and Sadeghi, J. (2008), “Adomian decomposition method and two coupled scalar fields”, Balan, V. (Ed.), in Balkan Society of Geometers (BSG) Proceedings of the 15th International Conference on “Differential Geometry and Dynamical Systems” (DGDS-2007), Bucharest, Romania, October 5-7, 2007, Geometry Balkan Press, Bucharest, Romania, pp. 11-18, available at: www.mathem.pub.ro/proc/bsgp-15/P-AM.pdf

Andrianov, I.V., Olevskii, V.I. and Tokarzewski, S. (1998), “A modified Adomian’s decomposition method”, Journal of Applied Mathematics and Mechanics, Vol. 62 No. 2, pp. 309-14.

Arenas, A.J., González-Parra, G., Jódar, L. and Villanueva, R.J. (2009), “Piecewise finite series solution of nonlinear initial value differential problem”, Applied Mathematics and Computation, Vol. 212 No. 1, pp. 209-15.

Arora, H. and Abdelwahid, F. (1993), “Solution of non-integer order differential equations via the Adomian decomposition method”, Applied Mathematics Letters, Vol. 6 No. 1, pp. 21-3.

Aslanov, A. (2009), “Approximate solutions of Emden-Fowler type equations”, International Journal of Computer Mathematics, Vol. 86 No. 5, pp. 807-826.

Arslanturk, C. (2005), “A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity”, International Communications in Heat and Mass Transfer, Vol. 32 No. 6, pp. 831-41.

Asil, V., Bulut, H. and Evans, D.J. (2004), “On the oscillatory solutions of nonlinear hyperbolic differential equations by the decomposition method”, International Journal of Computer Mathematics, Vol. 81 No. 5, pp. 639-45.

Asil, V., Bulut, H. and Evans, D.J. (2005), “The Adomian decomposition method for the approximate solution of homogeneous differential equations with dual variable and dual coefficients”, International Journal of Computer Mathematics, Vol. 82 No. 8, pp. 977-86.

Aslanov, A. and Abu-Alshaikh, I. (2008), “Further developments to the decomposition method for solving singular initial-value problems”, Mathematical and Computer Modelling, Vol. 48 Nos 5/6, pp. 700-11.

Attili, B.S. (2005), “The Adomian decomposition method for computing eigenelements of Sturm-Liouville two point boundary value problems”, Applied Mathematics and Computation, Vol. 168 No. 2, pp. 1306-16.

Attili, B.S. and Lesnic, D. (2006), “An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems”, Applied Mathematics and Computation, Vol. 182 No. 2, pp. 1247-54.

Azreg-Aïnou, M. (2009), “A developed new algorithm for evaluating Adomian polynomials”, CMES: Computer Modeling in Engineering and Sciences, Vol. 42 No. 1, pp. 1-18.

Azreg-Aïnou, M. (2010), “Developed Adomian method for quadratic Kaluza-Klein relativity”, Classical and Quantum Gravity, Vol. 27 No. 1, doi:10.1088/0264-9381/27/1/015012.

Az-Zo’bi, E.A. and Al-Khaled, K. (2010), “A new convergence proof of the Adomian decomposition method for a mixed hyperbolic elliptic system of conservation laws”, Applied Mathematics and Computation, Vol. 217 No. 8, pp. 4248-56.

Babajee, D.K.R., Dauhoo, M.Z., Darvishi, M.T., and Barati, A. (2008), “A note on the local convergence of iterative methods based on Adomian decomposition method and 3-node quadrature rule”, Applied Mathematics and Computation, Vol. 200 No. 1, pp. 452-8.

Babolian, E. and Biazar, J. (2002a), “On the order of convergence of Adomian method”, Applied Mathematics and Computation, Vol. 130 Nos. 2/3, pp. 383-7.

Babolian, E. and Biazar, J. (2002b) “Solution of nonlinear equations by modified Adomian decomposition method”, Applied Mathematics and Computation, Vol. 132 No. 1, pp. 167-72.

Babolian, E. and Biazar, J. (2002c), “Solving the problem of biological species living together by Adomian decomposition method”, Applied Mathematics and Computation, Vol. 129 Nos 2/3, pp. 339-43.

Babolian, E. and Biazar, J. (2003), “Solving concrete examples by Adomian method”, Applied Mathematics and Computation, Vol. 135 No. 1, pp. 161-7.

Babolian, E., Biazar, J. and Vahidi, A.R. (2004a), “A new computational method for Laplace transforms by decomposition method”, Applied Mathematics and Computation, Vol. 150 No. 3, pp. 841-6.

Babolian, E., Biazar, J. and Vahidi, A.R. (2004b), “Solution of a system of nonlinear equations by Adomian decomposition method”, Applied Mathematics and Computation, Vol. 150 No. 3, pp. 847-54.

Babolian, E., Biazar, J. and Vahidi, A.R. (2004c), “The decomposition method applied to systems of Fredholm integral equations of the second kind”, Applied Mathematics and Computation, Vol. 148 No. 2, pp. 443-52.

Babolian, E. and Davari, A. (2004), “Numerical implementation of Adomian decomposition method”, Applied Mathematics and Computation, Vol. 153 No. 1, pp. 301-5.

Babolian, E. and Davari, A. (2005), “Numerical implementation of Adomian decomposition method for linear Volterra integral equations of the second kind”, Applied Mathematics and Computation, Vol. 165 No. 1, pp. 223-7.

Babolian, E., Goghary, H.S., Javadi, Sh. and Ghasemi, M. (2005), “Restarted Adomian method for nonlinear differential equations”, International Journal of Computer Mathematics, Vol. 82 No. 1, pp. 97-102.

Babolian, E. and Javadi, Sh. (2003), “Restarted Adomian method for algebraic equations”, Applied Mathematics and Computation, Vol. 146 Nos 2/3, pp. 533-41.

Babolian, E. and Javadi, Sh. (2004), “New method for calculating Adomian polynomials”, Applied Mathematics and Computation, Vol. 153 No. 1, pp. 253-9.

Babolian, E., Javadi, Sh. and Sadeghi, H. (2004), “Restarted Adomian method for integral equations”, Applied Mathematics and Computation, Vol. 153 No. 2, pp. 353-9.

Babolian, E., Sadeghi, H. and Javadi, Sh. (2004), “Numerically solution of fuzzy differential equations by Adomian method”, Applied Mathematics and Computation, Vol. 149 No. 2, pp. 547-57.

Babolian, E., Vahidi, A.R. and Cordshooli, Gh.A. (2005), “Solving differential equations by decomposition method”, Applied Mathematics and Computation, Vol. 167 No. 2, pp. 1150-5.

Badredine, T., Abbaoui, K. and Cherruault, Y. (1999), “Convergence of Adomian’s method applied to integral equations”, Kybernetes, Vol. 28 No. 5, pp. 557-64.

Baghdasarian, A. (1991), “Comments on the validity of a proposed counterexample on the method of decomposition”, Mechanics Research Communications, Vol. 18 No. 1, pp. 67-9.

Baker, R. and Zeitoun, D.G. (1990), “Application of Adomian’s decomposition procedure to the analysis of a beam on random winkler support”, International Journal of Solids and Structures, Vol. 26 No. 2, pp. 217-35.

Banerjee, A., Bhattacharya, B. and Mallik, A.K. (2008), “Large deflection of cantilever beams with geometric non-linearity: analytical and numerical approaches”, International Journal of Non-Linear Mechanics, Vol. 43 No. 5, pp. 366-76.

Basak, K.C., Ray, P.C. and Bera, R.K., (2009) “Solution of non-linear Klein-Gordon equation with a quadratic non-linear term by Adomian decomposition method”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14 No. 3, pp. 718-23.

Basto, M., Semiao, V. and Calheiros, F.L. (2007), “Numerical study of modified Adomian’s method applied to Burgers equation”, Journal of Computational and Applied Mathematics, Vol. 206 No. 2, pp. 927-49.

Behiry, S.H., Abd-Elmonem, R.A. and Gomaa, A.M. (2010), “Discrete Adomian decomposition solution of nonlinear Fredholm integral equation”, Ain Shams Engineering Journal, Vol. 1 No. 1, pp. 97-101.

Behiry, S.H., Hashish, H., El-Kalla, I.L. and Elsaid, A. (2007), “A new algorithm for the decomposition solution of nonlinear differential equations”, Computers and Mathematics with Applications, Vol. 54 No. 4, pp. 459-66.

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Bellomo, N. and Monaco, R. (1985), “A comparison between Adomian’s decomposition methods and perturbation techniques for nonlinear random differential equations”, Journal of Mathematical Analysis and Applications, Vol. 110 No. 2, pp. 495-502.

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Bellomo, N. and Sarafyan, D. (1987), “On Adomian’s decomposition method and some comparisons with Picard’s iterative scheme”, Journal of Mathematical Analysis and Applications, Vol. 123 No. 2, pp. 389-400.

Benabidallah, M. and Cherruault, Y. (2004a), “Application of the Adomian method for solving a class of boundary problems”, Kybernetes, Vol. 33 No. 1, pp. 118-32.

Benabidallah, M. and Cherruault, Y. (2004b), “Solving a class of linear partial differential equations with Dirichlet-boundary conditions by the Adomian method”, Kybernetes, Vol. 33 No. 8, pp. 1292-1311.

Benabidallah, M. and Cherruault, Y. (2004c), “Using the Adomian method for solving a class of boundary differential systems”, Kybernetes, Vol. 33 No. 7, pp. 1185-204.

Beni, Y.T., Abadyan, M. and Noghrehabadi, A. (2011), “Investigation of size effect on the pull-in instability of beam-type NEMS under van der Waals attraction”, Procedia Engineering, Vol. 10, pp. 1718-23.

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Wazwaz, A.-M. (2001j), “Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method”, Chaos, Solitons and Fractals, Vol. 12 No. 12, pp. 2283-93.

Wazwaz, A.-M. (2001k), “Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method”, Chaos, Solitons and Fractals, Vol. 12 No. 8, pp. 1549-56.

Wazwaz, A.-M. (2001l), “Exact solutions to nonlinear diffusion equations obtained by the decomposition method”, Applied Mathematics and Computation, Vol. 123 No. 1, pp. 109-22.

Wazwaz, A.-M. (2001m), “The modified decomposition method applied to unsteady flow of gas through a porous medium”, Applied Mathematics and Computation, Vol. 118 Nos 2/3, pp. 123-32.

Wazwaz, A.-M. (2001n), “Analytic treatment for variable coefficient fourth-order parabolic partial differential equations”, Applied Mathematics and Computation, Vol. 123 No. 2, pp. 219-27.

Wazwaz, A.-M. (2001o), “A reliable algorithm for higher-dimensional diffusion equation subject to the specification of mass”, International Journal of Applied Mathematics, Vol. 7 No. 3, pp. 265-73.

Wazwaz, A.-M. (2002a), “A new method for solving singular initial value problems in the second-order ordinary differential equations”, Applied Mathematics and Computation, Vol. 128 No. 1, pp. 45-57.

Wazwaz, A.-M. (2002b), “A reliable treatment for mixed Volterra-Fredholm integral equations”, Applied Mathematics and Computation, Vol. 127 Nos 2/3, pp. 405-14.

Wazwaz, A.-M. (2002c), “The numerical solution of special fourth-order boundary value problems by the modified decomposition method”, International Journal of Computer Mathematics, Vol. 79 No. 3, pp. 345-56.

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Wazwaz, A.-M. (2003a), “An analytic study on the third-order dispersive partial differential equations”, Applied Mathematics and Computation, Vol. 142, Nos 2/3, pp. 511-20.

Wazwaz, A.-M. (2003b), “The existence of noise terms for systems of inhomogeneous differential and integral equations”, Applied Mathematics and Computation, Vol. 146, No. 1, pp. 81-92.

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Wazwaz, A.-M. (2005b), “Adomian decomposition method for a reliable treatment of the Emden-Fowler equation, Applied Mathematics and Computation, Vol. 161, No. 2, pp. 543-60.

Wazwaz, A.-M. (2005c), “Analytical solution for the time-dependent Emden-Fowler type of equations by Adomian decomposition method”, Applied Mathematics and Computation, Vol. 166 No. 3, pp. 638-51.

Wazwaz, A.-M. (2005d), “The modified decomposition method for analytic treatment of non-linear integral equations and systems of non-linear integral equations”, International Journal of Computer Mathematics, Vol. 82 No. 9, pp. 1107-15.

Wazwaz, A.-M. (2006a), “A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations”, Applied Mathematics and Computation, Vol. 181 No. 2, pp. 1703-12.

Wazwaz, A.-M. (2006b), “Padé approximants and Adomian decomposition method for solving the Flierl-Petviashivili equation and its variants”, Applied Mathematics and Computation, Vol. 182 No. 2, pp. 1812-8.

Wazwaz, A.-M. (2006c), “The modified decomposition method and Padé approximants for a boundary layer equation in unbounded domain”, Applied Mathematics and Computation, Vol. 177 No. 2, pp. 737-44.

Wazwaz, A.-M. (2006d), “The modified decomposition method for analytic treatment of differential equations”, Applied Mathematics and Computation, Vol. 173 No. 1, pp. 165-76.

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Further reading

Adomian, G. (1983), Stochastic Systems, Academic Press, New York, NY.

Adomian, G. (1986), Nonlinear Stochastic Operator Equations, Academic Press, Orlando, FL.

(1987),

Adomian, G. (1989), Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers, Dordrecht.

Adomian, G. (1994), Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Dordrecht.

Bellman, R.E. and Adomian, G. (1985), Partial Differential Equations: New Methods for their Treatment and Solution, D. Reidel Publishing Co., Dordrecht, pp. 237-87.

Bellomo, N. and Riganti, R. (1987), Nonlinear Stochastic System Analysis in Physics and Mechanics, World Scientific Publishing Co., Singapore and River Edge, NJ.

Cherruault, Y. (1998), Modèles et méthodes mathématiques pour les sciences du vivant, Presses Universitaires de France, Paris, pp. 119-61, 256-64.

Grzymkowski, R. (2010), Nieklasyczne metody rozwięzywania zagadnień przewodzenia ciepła, Wydawnictwo Politechniki Ślęskiej, Gliwice, pp. 142-87.

Grzymkowski, R., Hetmaniok, E. and Słota, D. (2002), Wybrane metody obliczeniowe w rachunku wariacyjnym oraz w równaniach róóniczkowych i całkowych, Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego, Gliwice, pp. 173-246.

Serrano, S.E. (1997), Hydrology for Engineers, Geologists and Environmental Professionals: An Integrated Treatment of Surface, Subsurface, and Contaminant Hydrology, HydroScience Inc., Lexington, KY.

Serrano, S.E. (2001), Engineering Uncertainty and Risk Analysis: A Balanced Approach to Probability, Statistics, Stochastic Modeling, and Stochastic Differential Equations, HydroScience Inc., Lexington, KY.

Serrano, S.E. (2010), Hydrology for Engineers, Geologists, and Environmental Professionals: An Integrated Treatment of Surface, Subsurface, and Contaminant Hydrology, 2nd revised ed., HydroScience Inc., Ambler, PA.

Serrano, S.E. (2011), Engineering Uncertainty and Risk Analysis: A Balanced Approach to Probability, Statistics, Stochastic Processes, and Stochastic Differential Equations, 2nd revised ed., HydroScience Inc., Ambler, PA.

Shingareva, I. and Lizárraga-Celaya, C. (2011), Solving Nonlinear Partial Differential Equations with Maple and Mathematica, Springer, New York, NY, pp. 227-42.

Wazwaz, A.-M. (1997), A First Course in Integral Equations, World Scientific Publishing Co., Singapore and River Edge, NJ.

Wazwaz, A.-M. (2002), Partial Differential Equations: Methods and Applications, A.A. Balkema, Lisse.

Wazwaz, A.-M. (2009), Partial Differential Equations and Solitary Waves Theory, Higher Education Press, Beijing, and Springer, Berlin.

Wazwaz, A.-M. (2011), Linear and Nonlinear Integral Equations: Methods and Applications, Higher Education Press, Beijing and Springer, Berlin.

Randolph Rach316, South Naple Street, Hartford, Michigan 49057-1225, USA E-mail: tapstrike@triton.net

Acknowledgments

The author is grateful to the Adomian family for their kindness and particularly would like to thank Mrs Corinne Adomian, Mrs Laura Adomian David and Mr William David, Athens, Georgia, USA for their generous assistance with access to Professor George Adomian’s extensive files to locate copies of his publications through the years. The author also appreciates the generous assistance from his friends and colleagues in locating research papers on the theory and applications of the Adomian decomposition method to enhance this developing worldwide, constructive bibliography, including especially Dr Abdul-Majid Wazwaz, Saint Xavier University, Chicago, Illinois, USA, Dr Sergio E. Serrano, Temple University, Philadelphia, Pennsylvania, USA, Dr Jun-Sheng Duan, Shanghai Institute of Technology, Shanghai, China, Dr Yan-Ping Sun, Taiyuan University of Technology, Taiyuan, China, Dr Yezhi Lin, East China Normal University, Shanghai, China, Dr Mehdi Dehghan, Amirkabir University of Technology, Tehran, Iran, Dr Daniel Lesnic, University of Leeds, Leeds, UK, Dr Damian Słota, Silesian University of Technology, Gliwice, Poland, Dr Luis Casasús and Dr Waleed Al-Hayani, Polytechnic University of Madrid, Madrid, Spain, Dr Paulo Rebelo, University of Beira Interior, Covilhã, Portugal and Dr José M. Machado, São Paulo State University, São José do Rio Preto, Brazil. Feci quod potui, faciant meliora potentes.

About the author

Randolph Rach is retired and formerly a Senior Engineer at Microwave Laboratories Inc. His experience includes research and development in microwave electronics and travelling-wave tube technology. He has both authored and co-authored 76 papers in applied mathematics and is an early contributor to the Adomian decomposition method. His current research interests include nonlinear systems analysis, nonlinear ordinary and partial differential equations, nonlinear integral equations, and nonlinear boundary value problems. Randolph Rach can be contacted at: tapstrike@triton.net