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

共 50 条

[21] Strong Stability Preserving Runge-Kutta and Linear Multistep Methods
Izzo, Giuseppe
Jackiewicz, Zdzislaw
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2022, 48 (06) : 4029 - 4062
[22] Stability of Runge-Kutta methods for linear delay differential equations
S. Maset
Numerische Mathematik, 2000, 87 : 355 - 371
[23] Construction of general linear methods with Runge-Kutta stability properties
Butcher, JC
Jackiewicz, Z
NUMERICAL ALGORITHMS, 2004, 36 (01) : 53 - 72
[24] Explicit general linear methods with inherent Runge-Kutta stability
Wright, WM
NUMERICAL ALGORITHMS, 2002, 31 (1-4) : 381 - 399
[25] SELF STARTING GENERAL LINEAR METHODS WITH RUNGE-KUTTA STABILITY
Izzo, Giuseppe
Jackiewicz, Zdzislaw
JOURNAL OF COMPUTATIONAL DYNAMICS, 2025, 12 (01): : 1 - 22
[26] STABILITY OF EXPLICIT RUNGE-KUTTA METHODS
SHAMPINE, LF
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1984, 10 (06) : 419 - 432
[27] Exponentially Fitted Symplectic Runge-Kutta-Nystrom Methods Derived by Partitioned Runge-Kutta Methods
Monovasilis, Th.
Kalogiratou, Z.
Simos, T. E.
11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013, PTS 1 AND 2 (ICNAAM 2013), 2013, 1558 : 1181 - 1185
[28] Symmetric Runge-Kutta methods and their stability
Kulikov, GY
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 2003, 18 (01) : 13 - 41
[29] Symplectic Partitioned Runge-Kutta And Symplectic Runge-Kutta Methods Generated By 2-Stage RadauIA Method
Tan, Jiabo
ADVANCES IN COMPUTATIONAL MODELING AND SIMULATION, PTS 1 AND 2, 2014, 444-445 : 633 - 636
[30] Symplectic Partitioned Runge-Kutta And Symplectic Runge-Kutta Methods Generated By 2-Stage LobattoIIIA Method
Tan, Jiabo
INTERNATIONAL CONFERENCE ON COMPUTATIONAL AND INFORMATION SCIENCES (ICCIS 2014), 2014, : 1069 - 1073

← 1 2 3 4 5 →