Title: A robust second order numerical method for a weakly coupled system of singularly perturbed reaction-diffusion problem with discontinuous source term
Authors: Pathan Mahabub Basha; Vembu Shanthi
Addresses: Department of Mathematics, National Institute of Technology, Tiruchirappalli-620015, Tamil Nadu, India ' Department of Mathematics, National Institute of Technology, Tiruchirappalli-620015, Tamil Nadu, India
Abstract: In this paper, a fitted mesh numerical method on Shishkin mesh is proposed to solve a weakly coupled system of two singularly perturbed reaction-diffusion equations containing equal diffusion parameters with discontinuous source terms. This method uses the standard centred finite difference scheme constructed on piecewise-uniform Shishkin mesh with the average of the source terms on either side of the point of discontinuity and then the problem is solved by an iterative procedure. An error analysis is carried out and the method ensures that the parameter-uniform convergence of almost the second order. Numerical results are provided to confirm the theoretical results and compares well with the existing results.
Keywords: singular perturbation problem; SPP; weakly coupled reaction-diffusion system; fitted mesh method; Shishkin mesh; discontinuous source term; parameter-uniform.
International Journal of Computing Science and Mathematics, 2020 Vol.11 No.1, pp.63 - 80
Received: 18 Aug 2017
Accepted: 27 Sep 2017
Published online: 27 Feb 2020 *