Splitting methods for non-autonomous Hamiltonian equations

被引：35

作者：

Blanes, S ^{[1
]}

Moan, PC ^{[1
]}

机构：

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 9EW, England

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2001年 / 170卷 / 01期

关键词：

non-linear time-dependent differential equations; initial value problems; numerical methods; free Lie algebra; Magnus expansion; symplectic;

D O I：

10.1006/jcph.2001.6733

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We present an algorithm for numerically integrating non-autonomous Hamiltonian differential equations. Special attention is paid to the separable case and, in particular, a new fourth-order splitting method is presented which in a certain measure is optimal. In combination with a new way of handling non-autonomous problems, the schemes we present are based on Magnus expansions and they show very promising results when applied to Hamiltonian ODEs and PDEs. (C) 2001 Academic Press.

引用

页码：205 / 230

页数：26

共 30 条

[1]

Arnold V.I., 1989, MATH METHODS CLASSIC, Vsecond

[2] Splitting methods for the time-dependent Schrodinger equation [J].

Blanes, S ;

Moan, PC .

PHYSICS LETTERS A, 2000, 265 (1-2) :35-42

[3] Improved high order integrators based on the Magnus expansion [J].

Blanes, S ;

Casas, F ;

Ros, J .

BIT NUMERICAL MATHEMATICS, 2000, 40 (03) :434-450

[4] Magnus and Fer expansions for matrix differential equations: The convergence problem [J].

Blanes, S ;

Casas, F ;

Oteo, JA ;

Ros, J .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (01) :259-268

[5] Symplectic integration with processing: A general study [J].

Blanes, S ;

Casas, F ;

Ros, J .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 21 (02) :711-727

[6] Processing symplectic methods for near-integrable Hamiltonian systems [J].

Blanes, S ;

Casas, F ;

Ros, J .

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2000, 77 (01) :17-35

[7]

BLANES S, 2000, 2000NA13 DAMTP U CAM

[8] A SYMPLECTIC INTEGRATION ALGORITHM FOR SEPARABLE HAMILTONIAN FUNCTIONS [J].

CANDY, J ;

ROZMUS, W .

JOURNAL OF COMPUTATIONAL PHYSICS, 1991, 92 (01) :230-256

[9] AN EXPLICIT SYMPLECTIC INTEGRATION SCHEME FOR PLASMA SIMULATIONS [J].

CARY, JR ;

DOXAS, I .

JOURNAL OF COMPUTATIONAL PHYSICS, 1993, 107 (01) :98-104

[10] AN EFFICIENT APPROXIMATION METHOD FOR STOCHASTIC DIFFERENTIAL-EQUATIONS BY MEANS OF THE EXPONENTIAL LIE SERIES [J].

CASTELL, F ;

GAINES, J .

MATHEMATICS AND COMPUTERS IN SIMULATION, 1995, 38 (1-3) :13-19

← 1 2 3 →