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
收藏
页码：232 / 263
页数：32
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