Title: A robust computational method for singularly perturbed system of 2D parabolic convection-diffusion problems
Authors: Maneesh Kumar Singh; Srinivasan Natesan
Addresses: Department of Mathematics, Indian Institute of Technology, Guwahati 781 039, India ' Department of Mathematics, Indian Institute of Technology, Guwahati 781 039, India
Abstract: This article presents a numerical scheme to solve singularly perturbed system of 2D parabolic convection-diffusion problem exhibiting exponential boundary layers. The numerical scheme consists of a fractional implicit-Euler scheme on uniform mesh for time discretisation and the classical upwind scheme on a piecewise uniform Shishkin mesh for spatial discretisation. For the proposed scheme, the stability analysis is presented and parameter-uniform error estimates are derived. It is shown that the numerical scheme is uniformly convergent with respect to the singular perturbation parameter. The proposed method is applied to a test problem to verify theoretical results numerically.
Keywords: singularly perturbed system; 2D parabolic problems; boundary layers; Shishkin meshes; finite difference scheme; fractional implicit-Euler method; uniform convergence.
International Journal of Mathematical Modelling and Numerical Optimisation, 2019 Vol.9 No.2, pp.127 - 157
Received: 04 Dec 2017
Accepted: 20 Mar 2018
Published online: 28 Jan 2019 *