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A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem

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  • Shifang Tian
  • Xiaowei Liu
  • Ran An

Abstract

In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and a hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform mesh and the backward Euler scheme are used for the temporal discretization. Furthermore, a preconditioning approach is also used to ensure uniform convergence. Numerical experiments show that the method is first-order accuracy in time and almost third-order accuracy in space.

Suggested Citation

  • Shifang Tian & Xiaowei Liu & Ran An, 2021. "A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-11, August.
    • Handle: RePEc:hin:jnlmpe:9941692
    DOI: 10.1155/2021/9941692
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