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LINEAR STABILITY OF PARTITIONED RUNGE-KUTTA METHODS
McLachlan, R. I.1; Sun, Y.2; Tse, P. S. P.2
2011
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume49Issue:1Pages:232-263
AbstractWe study the linear stability of partitioned Runge-Kutta (PRK) methods applied to linear separable Hamiltonian ODEs and to the semidiscretization of certain Hamiltonian PDEs. We extend the work of Jay and Petzold [Highly Oscillatory Systems and Periodic Stability, Preprint 95-015, Army High Performance Computing Research Center, Stanford, CA, 1995] by presenting simplified expressions of the trace of the stability matrix, tr M(s), for the Lobatto IIIA-IIIB family of symplectic PRK methods. By making the connection to Pade approximants and continued fractions, we study the asymptotic behavior of tr M(s)(w) as a function of the frequency w and stage number s.
Keywordasymptotic behavior continued fractions linear stability Lobatto IIIA-IIIB methods Pade approximants trace of stability matrix
DOI10.1137/100787234
Language英语
Funding ProjectRoyal Society of New Zealand ; National Natural Science Foundation of China[60931002] ; National Basic Research Program of China[2010CB832702] ; China Postdoctoral Science Foundation
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000287696800011
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12546
Collection计算数学与科学工程计算研究所
Affiliation1.Massey Univ, IFS, Palmerston North, New Zealand
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
McLachlan, R. I.,Sun, Y.,Tse, P. S. P.. LINEAR STABILITY OF PARTITIONED RUNGE-KUTTA METHODS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2011,49(1):232-263.
APA McLachlan, R. I.,Sun, Y.,&Tse, P. S. P..(2011).LINEAR STABILITY OF PARTITIONED RUNGE-KUTTA METHODS.SIAM JOURNAL ON NUMERICAL ANALYSIS,49(1),232-263.
MLA McLachlan, R. I.,et al."LINEAR STABILITY OF PARTITIONED RUNGE-KUTTA METHODS".SIAM JOURNAL ON NUMERICAL ANALYSIS 49.1(2011):232-263.
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