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

• Published in: Kybernetes Vol. 42; no. 4; pp. 641 - 664
• Main Authors: Bougoffa, Lazhar, Rach, Randolph C.
• Format: Journal Article
• Language: English
• Published: London Emerald Group Publishing Limited 19.04.2013
• Subjects: Algorithms; Boundary value problems; Decomposition; Differential equations; Finite element analysis; Integrals; Mathematical analysis; Mathematics; Nonlinearity; Studies; Transforms; Sturm-Liouville boundary value problems; Adomian polynomials; Adomian decomposition method; Nonlinear differential equations; Differential equations; Polynomials; Nonlocal boundary value problems
• ISSN: 0368-492X; 1758-7883
• DOI: 10.1108/K-09-2012-0045

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.