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

Author： Bougoffa Lazhar Rach Randolph C.

Publisher： Emerald Group Publishing Ltd

ISSN： 0368-492X

Source： Kybernetes: The International Journal of Systems & Cybernetics, Vol.42, Iss.4, 2013-04, pp. : 641-664

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

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.