Stability of variable-step BDF2 and BDF3 methods
Numerical Analysis
2023-01-31 v1 Numerical Analysis
Abstract
We prove that the two-step backward differentiation formula (BDF2) method is stable on arbitrary time grids; while the variable-step BDF3 scheme is stable if almost all adjacent step ratios are less than 2.553. These results relax the severe mesh restrictions in the literature and provide a new understanding of variable-step BDF methods. Our main tools include the discrete orthogonal convolution kernels and an elliptic-type matrix norm.
Cite
@article{arxiv.2201.00527,
title = {Stability of variable-step BDF2 and BDF3 methods},
author = {Zhaoyi Li and Hong-lin Liao},
journal= {arXiv preprint arXiv:2201.00527},
year = {2023}
}
Comments
20 pages, 2 figures, 3 tables