An effective numerical method for solving nonlinear second-order boundary value problems

Abstract

In this paper, we present an efficient numerical algorithm for approximate solutions of nonlinear second-order boundary value problems. We use the Laplace transform decomposition method to develop a new method for computing an approximate solution for nonlinear second-order boundary value problems. The Adomian decomposition method (shortly, ADM) together with the application of Laplace transform integral operator are applied to the differential equation. The new approach provides the solution in the form of a convergence series. An iterative algorithm is constructed for the determination of the infinite series solution.  Numerical results are included to demonstrate the reliability and efficiency of the proposed scheme. Comparison between exact and approximate solutions with known results is made.