A robust numerical scheme for singularly perturbed parabolic reaction-diffusion problems

Authors:
Srinivasan Natesan;Rajdeep Deb
Affiliations:
Department of Mathematics, Indian Institute of Technology, Guwahuti, India and Department of Chemical Engineering, Indian Institute of Technology, Guwahati, India;Department of Mathematics, Indian Institute of Technology, Guwahuti, India and Department of Chemical Engineering, Indian Institute of Technology, Guwahati, India
Venue:
Neural, Parallel & Scientific Computations
Year:
2008

Citing 4
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Abstract

In this article, we study the numerical solution of singularly perturbed parabolic reaction-diffusion initial-boundary-value problems. To solve these problems, we develop a numerical scheme which combines the cubic spline scheme and the classical finite difference scheme for the spatial derivatives, and backward difference scheme for the time derivative. To resolve the boundary layers, we use the piecewise uniform Shishkin mesh for the spatial discretization. Stability analysis and error estimates are obtained. The proposed method is applied to a test problem, which shows the parameter-uniform convergent results.