A method for an approximate numerical solution of two-point boundary value problems: nonstandard finite difference method on a semi-open interval. (6th June 2023)

• Record Type: Journal Article
• Authors: Pandey, Pramod Kumar
• Is Part Of: International journal of computing science and mathematics. Volume 17:Number 3(2023)
• Page Start: 220
• Page End: 228
• Publication Date: 2023-06-06
• Subjects: boundary value problem -- nonstandard finite difference -- quasi-uniform step length -- semi-open interval -- singular problem; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

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.