Online from: 1991
Subject Area: Mechanical & Materials Engineering
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|Title:||An efficient method for Cauchy problem of ill-posed nonlinear diffusion equation|
|Author(s):||Mashallah Matinfar, (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran), Mostafa Eslami, (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran), Mohammad Saeidy, (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran)|
|Citation:||Mashallah Matinfar, Mostafa Eslami, Mohammad Saeidy, (2013) "An efficient method for Cauchy problem of ill-posed nonlinear diffusion equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 Iss: 3, pp.427 - 435|
|Keywords:||Cauchy problem of nonlinear diffusion equation, Differential equations, Mathematics, New homotopy perturbation method|
|Article type:||Research paper|
|DOI:||10.1108/09615531311301227 (Permanent URL)|
|Publisher:||Emerald Group Publishing Limited|
Purpose – The purpose of this paper is to introduce a new homotopy perturbation method (NHPM) to solve Cauchy problem of unidimensional non-linear diffusion equation.
Design/methodology/approach – In this paper a modified version of HPM, which the authors call NHPM, has been presented; this technique performs much better than the HPM. HPM and NHPM start by considering a homotopy, and the solution of the problem under study is assumed to be as the summation of a power series in
Findings – In this article, the authors have applied the NHPM for solving nonlinear Cauchy diffusion equation. In comparison with the homotopy perturbation method (HPM), in the present method, the authors achieve exact solutions while HPM does not lead to exact solutions. The authors believe that the new method is a promising technique in finding the exact solutions for a wide variety of mathematical problems.
Originality/value – The basic idea described in this paper is expected to be further employed to solve other functional equations.
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