A method for an approximate numerical solution of two-point boundary value problems: nonstandard finite difference method on a semi-open interval
by Pramod Kumar Pandey
International Journal of Computing Science and Mathematics (IJCSM), Vol. 17, No. 3, 2023

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.

Online publication date: Tue, 13-Jun-2023

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