A robust computational method for singularly perturbed system of 2D parabolic convection-diffusion problems
by Maneesh Kumar Singh; Srinivasan Natesan
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 9, No. 2, 2019

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.

Online publication date: Tue, 02-Apr-2019

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