Volume preservation by Runge-Kutta methods

被引：3

作者：

Bader, Philipp ^{[1
]}

McLaren, David I. ^{[1
]}

Quispel, G. R. W. ^{[1
]}

Webb, Marcus ^{[2
]}

机构：

[1] La Trobe Univ, Dept Math & Stat, Bundoora, Vic 3086, Australia

[2] Univ Cambridge, DAMTP, Wilberforce Rd, Cambridge CB3 0WA, England

来源：

APPLIED NUMERICAL MATHEMATICS | 2016年 / 109卷

基金：

澳大利亚研究理事会; 英国工程与自然科学研究理事会;

关键词：

Volume preservation; Runge-Kutta method; Measure preservation; Kahan's method; DYNAMICAL-SYSTEMS; GEOMETRIC INTEGRATION;

D O I：

10.1016/j.apnum.2016.06.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is a classical theorem of Liouville that Hamiltonian systems preserve volume in phase space. Any symplectic Runge-Kutta method will respect this property for such systems, but it has been shown by Iserles, Quispel and Tse and independently by Chartier and Murua that no B-Series method can be volume preserving for all volume preserving vector fields. In this paper, we show that despite this result, symplectic Runge-Kutta methods can be volume preserving for a much larger class of vector fields than Hamiltonian systems, and discuss how some Runge-Kutta methods can preserve a modified measure exactly. (C) 2016 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：123 / 137

页数：15

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