Geometric properties of Kahan's method

被引：58

作者：

Celledoni, Elena ^{[1
]}

McLachlan, Robert I. ^{[2
]}

Owren, Brynjulf ^{[1
]}

Quispel, G. R. W. ^{[3
]}

机构：

[1] NTNU, Dept Math Sci, NO-7491 Trondheim, Norway

[2] Massey Univ, Inst Fundamental Sci, Palmerston North 4442, New Zealand

[3] La Trobe Univ, Dept Math, Bundoora, Vic 3083, Australia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2013年 / 46卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

HIROTA-KIMURA TYPE;

D O I：

10.1088/1751-8113/46/2/025201

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that Kahan's discretization of quadratic vector fields is equivalent to a Runge-Kutta method. When the vector field is Hamiltonian on either a symplectic vector space or a Poisson vector space with constant Poisson structure, the map determined by this discretization has a conserved modified Hamiltonian and an invariant measure, a combination previously unknown amongst Runge-Kutta methods applied to nonlinear vector fields. This produces large classes of integrable rational mappings in two and three dimensions, explaining some of the integrable cases that were previously known.

引用

页数：12