Title: A method for an approximate numerical solution of two-point boundary value problems: nonstandard finite difference method on a semi-open interval

Authors: Pramod Kumar Pandey

Addresses: Department of Mathematics, Dyal Singh College, University of Delhi, Lodhi Road, New Delhi, 110003, India

Abstract: In this paper, a nonstandard finite difference technique is considered with semi-uniform nodes for the numerical solution of the two-point boundary value problem subject to Dirichlet boundary conditions in the semi-open domain. To overcome the discretisation issue at the right open end of the domain, i.e., at infinity-semi-uniform nodes were used. The boundary condition at infinity is taken into account precisely by the so-generated semi uniform nodes. The numerical experiment with a proposed method carried out by considering model problems, including singular problems. The method proposed in the paper produces a decent approximate solution of the considered problems and totally conquers the issue of boundary conditions at infinity and singularity.

Keywords: boundary value problem; nonstandard finite difference; quasi-uniform step length; semi-open interval; singular problem.

DOI: 10.1504/IJCSM.2023.131455

International Journal of Computing Science and Mathematics, 2023 Vol.17 No.3, pp.220 - 228

Accepted: 23 Sep 2022
Published online: 13 Jun 2023 *

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