Stability of Variable-Step BDF2 and BDF3 Methods
نویسندگان
چکیده
We prove that the two-step backward differentiation formula (BDF) method is stable on arbitrary time grids; while variable-step three-step scheme if almost all adjacent step ratios are less than 2.553. These results relax severe mesh restrictions in literature and provide a new understanding of BDF methods. Our main tools include discrete orthogonal convolution kernels an elliptic type matrix norm.
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2022
ISSN: ['0036-1429', '1095-7170']
DOI: https://doi.org/10.1137/21m1462398