南方科技大学知识苑(SUSTech KC): A New Discrete Energy Technique for Multi-Step Backward Difference Formulas

题名	A New Discrete Energy Technique for Multi-Step Backward Difference Formulas
作者	Liao, Hong-Lin 1,2; Tang, Tao3,4 ; Zhou, Tao 5
通讯作者	Zhou, Tao
发表日期	2022-06-01
DOI	10.4208/csiam-am.SO-2021-0032
发表期刊	CSIAM TRANSACTIONS ON APPLIED MATHEMATICS 影响因子和分区
ISSN	2708-0560
EISSN	2708-0579
卷号	3 期号:2
摘要	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.
关键词	Linear diffusion equations backward differentiation formulas discrete orthogonal convolution kernels positive definiteness stability and convergence
相关链接	[来源记录]
收录类别	ESCI
语种	英语
学校署名	其他
资助项目	NSF of China[11822111,11688101,12071216,11731006,"K20911001","NNW2018-ZT4A06"] ; Science Challenge Project[TZ2018001] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA25000404]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000804100400006
出版者	GLOBAL SCIENCE PRESS
来源库	Web of Science
引用统计	被引频次[WOS]：12
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/343084
专题	南方科技大学
作者单位	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
推荐引用方式 GB/T 7714	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).
APA	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).
MLA	Liao, Hong-Lin,et al."A New Discrete Energy Technique for Multi-Step Backward Difference Formulas".CSIAM TRANSACTIONS ON APPLIED MATHEMATICS 3.2(2022).