TY  - JOUR
AB  - 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.
VL  - 42
IS  - 4
SN  - 0368-492X
DO  - 10.1108/K-09-2012-0045
UR  - https://doi.org/10.1108/K-09-2012-0045
AU  - Bougoffa Lazhar
AU  - Rach Randolph C.
PY  - 2013
Y1  - 2013/01/01
TI  - Solving nonlocal boundary value problems for first‐ and second‐order differential equations by the Adomian decomposition method
T2  - Kybernetes
PB  - Emerald Group Publishing Limited
SP  - 641
EP  - 664
Y2  - 2024/09/19
ER  -