Solving nonlocal boundary value problems for first‐ and second‐order differential equations by the Adomian decomposition method

Abstract

Purpose

The purpose of this paper is to present a new approach to solve nonlocal boundary value problems of linear and nonlinear first‐ and second‐order differential equations subject to nonlocal conditions of integral type.

Design/methodology/approach

The authors first transform the given nonlocal boundary value problems of first‐ and second‐order differential equations into local boundary value problems of second‐ and third‐order differential equations, respectively. Then a modified Adomian decomposition method is applied, which permits convenient resolution of these equations.

Findings

The new technique, as presented in this paper in extending the applicability of the Adomian decomposition method, has been shown to be very efficient for solving nonlocal boundary value problems of linear and nonlinear first‐ and second‐order differential equations subject to nonlocal conditions of integral type.

Originality/value

The paper presents a new solution algorithm for the nonlocal boundary value problems of linear and nonlinear first‐ and second‐order differential equations subject to nonlocal conditions of integral type.

Citation

Bougoffa, L. and Rach, R.C. (2013), "Solving nonlocal boundary value problems for first‐ and second‐order differential equations by the Adomian decomposition method", Kybernetes, Vol. 42 No. 4, pp. 641-664. https://doi.org/10.1108/K-09-2012-0045