A finite-difference scheme for a coupled system of singularly perturbed time-dependent reaction–diffusion equations with discontinuous source terms. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Aarthika, K.; Shanthi, V.; Ramos, Higinio
• Is Part Of: International journal of computer mathematics. Volume 98:Issue 1(2021)
• Page Start: 120
• Page End: 135
• Publication Date: 2021-01-02
• Subjects: Singularly perturbed problem -- finite-difference scheme -- reaction–diffusion system -- discontinuous source terms -- Shishkin mesh; 65N06 -- 65N22 -- 35B25; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2020.1733538
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this paper, a coupled system of singularly perturbed parabolic one-dimensional reaction–diffusion equations with discontinuous source terms is considered. To obtain a reliable approximation of the system solution, we construct a numerical method by using an effective finite-difference scheme which involves a suitable layer-adapted piecewise-uniform Shishkin mesh. We show that the approximations provided by the proposed numerical method converge uniformly with respect to the singular perturbation parameter. The performance of the singularly perturbed parabolic system successfully tested illustrates the agreement with the theoretical results.