Weighted and shifted BDF2 methods on variable grids
Abstract
Variable steps implicit-explicit multistep methods for PDEs have been presented in [17], where the zero-stability is studied for ODEs; however, the stability analysis still remains an open question for PDEs. Based on the idea of linear multistep methods, we present a simple weighted and shifted BDF2 methods with variable steps for the parabolic problems, which serve as a bridge between BDF2 and Crank-Nicolson scheme. The contributions of this paper are as follows: we first prove that the optimal adjacent time-step ratios for the weighted and shifted BDF2, which greatly improve the maximum time-step ratios for BDF2 in [11,15]. Moreover, the unconditional stability and optimal convergence are rigorous proved, which make up for the vacancy of the theory for PDEs in [17]. Finally, numerical experiments are given to illustrate theoretical results.
Cite
@article{arxiv.2108.02910,
title = {Weighted and shifted BDF2 methods on variable grids},
author = {Minghua Chen and Fan Yu and Qingdong Zhang},
journal= {arXiv preprint arXiv:2108.02910},
year = {2021}
}
Comments
19 pages, 6 figures