中文版 | English
Title

ON ENERGY LAWS AND STABILITY OF RUNGE-KUTTA METHODS FOR LINEAR SEMINEGATIVE PROBLEMS

Author
Publication Years
2022
DOI
Source Title
ISSN
0036-1429
EISSN
1095-7170
Volume60Issue:5Pages:2448-2481
Abstract
This paper presents a systematic theoretical framework to derive the energy identities of general implicit and explicit Runge-Kutta (RK) methods for linear seminegative systems. It generalizes the stability analysis of only explicit RK methods in [Z. Sun and C.-W. Shu, SIAM J. Numer. Anal., 57 (2019), pp. 1158-1182]. The established energy identities provide a precise characterization on whether and how the energy dissipates in the RK discretization, thereby leading to weak and strong stability criteria of RK methods. Furthermore, we discover a unified energy identity for all the diagonal Padé approximations, based on an analytical Cholesky type decomposition of a class of symmetric matrices. The structure of the matrices is very complicated, rendering the discovery of the unified energy identity and the proof of the decomposition highly challenging. Our proofs involve the construction of technical combinatorial identities and novel techniques from the theory of hypergeometric series. Our framework is motivated by a discrete analogue of integration by parts technique and a series expansion of the continuous energy law. In some special cases, our analyses establish a close connection between the continuous and discrete energy laws, enhancing our understanding of their intrinsic mechanisms. Several specific examples of implicit methods are given to illustrate the discrete energy laws. A few numerical examples further confirm the theoretical properties.
Keywords
URL[Source Record]
Indexed By
Language
English
SUSTech Authorship
Others
Funding Project
National Natural Science Foundation of China[12171227];Norsk Sykepleierforbund[DMS-2208391];
WOS Research Area
Mathematics
WOS Subject
Mathematics, Applied
WOS Accession No
WOS:000889757900004
Publisher
ESI Research Field
MATHEMATICS
Scopus EID
2-s2.0-85138470113
Data Source
Scopus
Citation statistics
Cited Times [WOS]:1
Document TypeJournal Article
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/402772
DepartmentDepartment of Mathematics
深圳国际数学中心(杰曼诺夫数学中心)(筹)
深圳国家应用数学中心
Affiliation
1.Department of Mathematics,The University of Alabama,Tuscaloosa,35487,United States
2.Department of Mathematics,Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
3.Department of Mathematics,SUSTech International Center for Mathematics,Southern University of Science and Technology,National Center for Applied Mathematics Shenzhen (NCAMS),Shenzhen,Guangdong,518055,China
Recommended Citation
GB/T 7714
Sun,Zheng,Wei,Yuanzhe,Wu,Kailiang. ON ENERGY LAWS AND STABILITY OF RUNGE-KUTTA METHODS FOR LINEAR SEMINEGATIVE PROBLEMS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2022,60(5):2448-2481.
APA
Sun,Zheng,Wei,Yuanzhe,&Wu,Kailiang.(2022).ON ENERGY LAWS AND STABILITY OF RUNGE-KUTTA METHODS FOR LINEAR SEMINEGATIVE PROBLEMS.SIAM JOURNAL ON NUMERICAL ANALYSIS,60(5),2448-2481.
MLA
Sun,Zheng,et al."ON ENERGY LAWS AND STABILITY OF RUNGE-KUTTA METHODS FOR LINEAR SEMINEGATIVE PROBLEMS".SIAM JOURNAL ON NUMERICAL ANALYSIS 60.5(2022):2448-2481.
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