A fixed point iteration method using Green's functions for the solution of nonlinear boundary value problems over semi-Infinite intervals

Abstract

ABSTRACTIn this paper, an iterative method is introduced for the numerical solution of a class of nonlinear two-point boundary value problems (BVPs) on semi-infinite intervals. The underlying strategy behind this novel approach is to construct a tailored integral operator that is expressed in terms of a Green's function for the corresponding linear differential operator of the BVP. Then, two well-known fixed point iterations, including Picard's and Krasnoselskii-Mann's schemes, are applied to this integral operator that results in this new iterative technique. A proof of convergence of the numerical scheme, based on the contraction principle, is included. We demonstrate the reliability, fast convergence, applicability of the method and compare its performance, using some relevant test examples that appear in the literature.