@Article{IJNAM-22-671,
author = {Chen , MinghuaYu , Fan and Zhang , Qingdong},
title = {The Weighted and Shifted Two-Step BDF Method for Allen-Cahn Equation on Variable Grids },
journal = {International Journal of Numerical Analysis and Modeling},
year = {2025},
volume = {22},
number = {5},
pages = {671--693},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2025-1029},
url = {http://global-sci.org/intro/article_detail/ijnam/24081.html}
}