Invariants preserving schemes based on explicit Runge–Kutta methods

被引：0
作者：
H. Kojima
机构：
[1] The University of Tokyo,Department of Mathematical Informatics, Graduate School of Information Science and Technology
来源：
BIT Numerical Mathematics | 2016年 / 56卷
关键词：
Initial value problems; Perturbed collocation methods ; Numerical geometric integration; Projection methods; Explicit Runge–Kutta methods; 65L05; 65L06;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Numerical integration of ordinary differential equations with some invariants is considered. For such a purpose, certain projection methods have proved its high accuracy and efficiency. Unfortunately, however, sometimes they can exhibit instability. In this paper, a new, highly efficient projection method is proposed based on explicit Runge–Kutta methods. The key there is to employ the idea of the perturbed collocation method, which gives a unified way to incorporate scheme parameters for projection. Numerical experiments confirm the stability of the proposed method.
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页码：1317 / 1337
页数：20
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