Year: 2022
Author: Hong-Lin Liao, Tao Tang, Tao Zhou
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 2 : pp. 318–334
Abstract
The backward differentiation formula (BDF) is a popular family of implicit methods for the numerical integration of stiff differential equations. It is well noticed that the stability and convergence of the $A$-stable BDF1 and BDF2 schemes for parabolic equations can be directly established by using the standard discrete energy analysis. However, such classical analysis seems not directly applicable to the BDF-k with 3 ≤ k ≤ 5. To overcome the difficulty, a powerful analysis tool based on the Nevanlinna-Odeh multiplier technique [Numer. Funct. Anal. Optim., 3:377-423, 1981] was developed by Lubich et al. [IMA J. Numer. Anal., 33:1365-1385, 2013]. In this work, by using the so-called discrete orthogonal convolution kernel technique, we recover the classical energy analysis so that the stability and convergence of the BDF-k with 3 ≤ k ≤ 5 can be established.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2021-0032
CSIAM Transactions on Applied Mathematics, Vol. 3 (2022), Iss. 2 : pp. 318–334
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Linear diffusion equations backward differentiation formulas discrete orthogonal convolution kernels positive definiteness stability and convergence.