A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem. (20th August 2021)

• Record Type: Journal Article
• Authors: Tian, Shifang; Liu, Xiaowei; An, Ran
• Other Names: Wang Hui Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-08-20
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/9941692
• Languages: English
• ISSNs: 1024-123X

Abstract

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.