Construction of Runge-Kutta methods of Crouch-Grossman type of high order

被引:9
作者
Jackiewicz, Z
Marthinsen, A
Owren, B
机构
[1] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway
[2] Arizona State Univ, Dept Math, Tempe, AZ 85287 USA
基金
美国国家科学基金会;
关键词
Runge-Kutta methods; order conditions; geometric integration; rigid frames; least squares minimization;
D O I
10.1023/A:1016645730465
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
An approach is described to the numerical solution of order conditions for Runge-Kutta methods whose solutions evolve on a given manifold. This approach is based on least squares minimization using the Levenberg-Marquardt algorithm. Methods of order four and five are constructed and numerical experiments are presented which confirm that the derived methods have the expected order of accuracy.
引用
收藏
页码:405 / 415
页数:11
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