Invariants preserving schemes based on explicit Runge–Kutta methods

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• 作者：H. Kojima
• 关键词：Initial value problems ; Perturbed collocation methods ; Numerical geometric integration ; Projection methods ; Explicit Runge–Kutta methods
• 刊名：BIT Numerical Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：56
• 期：4
• 页码：1317-1337
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Numeric Computing; Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1572-9125
• 卷排序：56

文摘

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.