Year: 2024
Author: Xiangyi Peng, Wenlin Qiu, Jiangxing Wang, Lina Ma
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1358–1380
Abstract
We present a novel two-grid compact finite difference scheme for the viscous Burgers’ equation in this paper, where the second-order Crank-Nicolson method is used to deal with the time marching, the compact finite difference formula is used to approximate the spatial second-order term, and the nonlinear convection term is discretized using the developed nonlinear fourth-order operator, providing the scheme with both high fourth-order spatial convergence and a low computational cost. The scheme is then established in three steps, with the first step being the construction of a nonlinear coarse-grid compact finite difference scheme that is solved iteratively using a fixed point iterative method, the second step being the application of the Lagrange interpolation formula to obtain a rough solution on the fine grid, and the third step being the development of the linearized fine-grid compact finite difference scheme. We also perform a convergence and stability analysis on the developed scheme, and the results show that the scheme can achieve spatial fourth-order and temporal second-order convergence. Finally, a number of numerical examples are provided to validate the theoretical predictions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0302
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 6 : pp. 1358–1380
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Two-grid compact finite difference viscous Burgers stability error analysis.
Author Details
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