LINEAR STABILITY OF PARTITIONED RUNGE-KUTTA METHODS

被引：15

作者：

McLachlan, R. I. ^{[1
]}

Sun, Y. ^{[2
]}

Tse, P. S. P. ^{[2
]}

机构：

[1] Massey Univ, IFS, Palmerston North, New Zealand

[2] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 01期

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

asymptotic behavior; continued fractions; linear stability; Lobatto IIIA-IIIB methods; Pade approximants; trace of stability matrix; HAMILTONIAN-SYSTEMS; INTEGRATORS; SCHEMES; ORDER;

D O I：

10.1137/100787234

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We 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.

引用

页码：232 / 263

页数：32

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