A fixed point iteration method using Green's functions for the solution of nonlinear boundary value problems over semi-Infinite intervals. Issue 6 (2nd June 2020)

• Record Type: Journal Article
• Authors: Khuri, S. A.; Sayfy, A.
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 6(2020)
• Page Start: 1303
• Page End: 1319
• Publication Date: 2020-06-02
• Subjects: Fixed point iterative schemes -- Green's function -- boundary value problems over semi-infinite domain -- mann iteration scheme -- Picard iteration scheme; 65L10; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1615618
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In 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.