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Richardson extrapolation technique for singularly perturbed system of parabolic partial differential equations with exponential boundary layers

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  • Singh, Maneesh Kumar
  • Natesan, Srinivasan

Abstract

In this article, we propose a higher-order uniformly convergent numerical scheme for singularly perturbed system of parabolic convection-diffusion problems exhibiting overlapping exponential boundary layers. It is well-known that the the numerical scheme consists of the backward-Euler method for the time derivative on uniform mesh and the classical upwind scheme for the spatial derivatives on a piecewise-uniform Shishkin mesh converges uniformly with almost first-order in both space ant time. Richardson extrapolation technique improves the accuracy of the above mentioned scheme from first-order to second-order uniformly convergent in both time and space. This has been proved mathematically in this article. In order to validate the theoretical results, we carried out some numerical experiments.

Suggested Citation

  • Singh, Maneesh Kumar & Natesan, Srinivasan, 2018. "Richardson extrapolation technique for singularly perturbed system of parabolic partial differential equations with exponential boundary layers," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 254-275.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:254-275
    DOI: 10.1016/j.amc.2018.03.059
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    Cited by:

    1. Singh, Satpal & Kumar, Devendra, 2023. "Parameter uniform numerical method for a system of singularly perturbed parabolic convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 360-381.

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