Year: 2025
Author: Minghua Chen, Fan Yu, Qingdong Zhang
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 5 : pp. 671–693
Abstract
The weighted and shifted seven-step BDF method is proposed by the authors [Akrivis, Chen, and Yu, IMA. Numer. Anal., DOI:10.1093/imanum/drae089] for parabolic equation on uniform meshes. In this paper, we study the weighted and shifted two-step BDF method (WSBDF2) for the Allen-Cahn equation on variable grids. In order to preserve a modified energy dissipation law at the discrete level, a novel technique is designed to deal with the nonlinear term. The stability and convergence analysis of the WSBDF2 method are rigorously proved by the energy method under the adjacent time-step ratios $r_s ≥ 4.8645.$ Finally, numerical experiments are implemented to illustrate the theoretical results. The proposed approach is applicable for the Cahn-Hilliard equation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1029
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 5 : pp. 671–693
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Weighted and shifted two-step BDF method variable step size Allen-Cahn equation stability and convergence analysis.