Analysis of a Fitted Finite Difference Scheme for a Semilinear System of Singularly Perturbed Reaction-Diffusion Equations Having Discontinuous Source Term. (29th September 2022)

• Record Type: Journal Article
• Authors: Chawla, Sheetal; Suhag, Urmil
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 13(2022)
• Page Start: 1511
• Page End: 1537
• Publication Date: 2022-09-29
• Subjects: Discontinuous source term -- finite difference scheme -- Green's function -- layer adapted meshes -- semilinear reaction-diffusion -- singularly perturbed; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2111576
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, a system of an arbitrary number of singularly perturbed semilinear differential equations of reaction-diffusion type having discontinuous source term is examined, for the case in which the diffusion parameters associated with each equation of the considered system are assumed to be different in magnitude. In addition to the occurrence of the boundary layers, the solution exhibits the overlapping and interacting internal layers due to the existence of discontinuity in the data. A central finite difference scheme is used in conjunction with a suitable piecewise uniform Shishkin mesh and a Bakhvalov mesh, to construct the numerical method. Using discrete Green's function technique, the proposed numerical scheme has been proved to be an almost second-order of uniform convergent for the Shishkin mesh and second-order of uniform convergent for the Bakhvalov mesh, independent of the perturbation parameters. Numerical test examples are presented to demonstrate the performance of the numerical scheme.