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

Shifang Tian, Xiaowei Liu and Ran An

Mathematical Problems in Engineering, 2021, vol. 2021, 1-11

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:9941692

DOI: 10.1155/2021/9941692

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