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
来源：
ADVANCES IN COMPUTATIONAL MATHEMATICS | 2000年 / 13卷 / 04期
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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