Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems

Authors:
Kaushik Mukherjee;Srinivasan Natesan
Affiliations:
Indian Institute of Technology Guwahati, Department of Mathematics, 781 039, Guwahati, India;Indian Institute of Technology Guwahati, Department of Mathematics, 781 039, Guwahati, India
Venue:
Computing
Year:
2009

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Abstract

In this paper, we propose a numerical scheme which is almost second-order spatial accurate for a one-dimensional singularly perturbed parabolic convection-diffusion problem exhibiting a regular boundary layer. The proposed numerical scheme consists of classical backward-Euler method for the time discretization and a hybrid finite difference scheme for the spatial discretization. We analyze the scheme on a piecewise-uniform Shishkin mesh for the spatial discretization to establish uniform convergence with respect to the perturbation parameter. Numerical results are presented to validate the theoretical results.