@Article{CSIAM-AM-3-2,
author = {Liao, Hong-Lin and Tao, Tang and Zhou, Tao},
title = {A New Discrete Energy Technique for Multi-Step Backward Difference Formulas},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2022},
volume = {3},
number = {2},
pages = {318--334},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2021-0032},
url = {https://global-sci.com/article/82320/a-new-discrete-energy-technique-for-multi-step-backward-difference-formulas}
}