A new efficient technique for solving two-point boundary value problems for integro-differential equations

Abstract

In this paper, we propose a new efficient method based on a combination of Adomian decomposition method (ADM) and Green’s function for solving second-order boundary value problems (BVPs) for integro-differential equations (IDEs). The proposed method depends on constructing Green’s function before establishing the recursive scheme for the solution components. Unlike the ADM or modified ADM , the proposed method avoids solving a sequence of difficult nonlinear equations (transcendental equations) for the unknown parameters. The proposed method provides a direct recursive scheme for obtaining the series solution with easily calculable components. We also provide a sufficient condition that guarantees a unique solution to the second-order BVPs for IDEs. Convergence and error analysis of the proposed method are also discussed. Convergence analysis is reliable enough to estimate the error bound of the series solution. Some numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed approach. The numerical results reveal that the proposed method is very effective and simple.