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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781 039, India

    Kaushik Mukherjee & Srinivasan Natesan

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  1. Kaushik Mukherjee
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  2. Srinivasan Natesan
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Correspondence to Srinivasan Natesan.

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Mukherjee, K., Natesan, S. Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems. Computing 84, 209–230 (2009). https://doi.org/10.1007/s00607-009-0030-2

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  • DOI: https://doi.org/10.1007/s00607-009-0030-2

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