A New Discrete Energy Technique for Multi-Step Backward Difference Formulas

Liao, Hong-Lin1,2; Tang, Tao3,4; Zhou, Tao5

2022-06-01

10.4208/csiam-am.SO-2021-0032

CSIAM TRANSACTIONS ON APPLIED MATHEMATICS   Impact Factor & Quartile

2708-0560

2708-0579

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.

Linear diffusion equations backward differentiation formulas discrete orthogonal convolution kernels positive definiteness stability and convergence

ESCI

English

Others

NSF of China[11822111,11688101,12071216,11731006,"K20911001","NNW2018-ZT4A06"] ; Science Challenge Project[TZ2018001] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA25000404]

Mathematics

Mathematics, Applied

WOS:000804100400006

GLOBAL SCIENCE PRESS

Web of Science

1.Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211106, Peoples R China
2.MIIT, Key Lab Math Modelling & High Performance Comp Ai, Nanjing 211106, Peoples R China
3.BNU HKBU United Int Coll, Div Sci & Technol, Zhuhai, Guangdong, Peoples R China
4.Southern Univ Sci & Technol, Int Ctr Math, Shenzhen, Guangdong, Peoples R China
5.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China

Liao, Hong-Lin,Tang, Tao,Zhou, Tao. A New Discrete Energy Technique for Multi-Step Backward Difference Formulas[J]. CSIAM TRANSACTIONS ON APPLIED MATHEMATICS,2022,3(2).

Liao, Hong-Lin,Tang, Tao,&Zhou, Tao.(2022).A New Discrete Energy Technique for Multi-Step Backward Difference Formulas.CSIAM TRANSACTIONS ON APPLIED MATHEMATICS,3(2).

Liao, Hong-Lin,et al."A New Discrete Energy Technique for Multi-Step Backward Difference Formulas".CSIAM TRANSACTIONS ON APPLIED MATHEMATICS 3.2(2022).