ORDER PROPERTIES AND CONSTRUCTION OF SYMPLECTIC RUNGE-KUTTA METHODS

• 来源期刊: 计算数学（英文版）
• 关键词: Numerical analysis Symplectic Runge-Kutta methods Simplifying conditions Order results.
• 年，卷（期）: 2000,（6）
• 页码范围: 645-656
• 页数: 12页
• 语种: 英文

摘要

The main results of this paper are as follows: (1) Suppose an s stage RungeKutta method is consistent, irreducible, non-confluent and symplectic. Then this method is of order at least 2p +l(1 < p < s - 1) provided that the simplifying conditions C(p) (or D(p) with non-zero weights) and B(2p + l) hold, where l=0, 1, 2. (2) Suppose an s stage Runge-Kutta method is consistent, irreducible and non-confluent, and satisfies the simplifying conditions C(p) and D(p) with 0 ＜ p <s. Then this method is symplectic if and only if either p = s or the nonlinear stability matrix M of the method has an (s - p) × (s - p) chief submatrix M =0. (3) Using the results (1) and (2) as bases, we present a general approach for the construction of symplectic Runge-Kutta methods, and a software has been designed, by means of which, the coefficients of s stage symplectic Runge-Kutta methods satisfying C(p), D(p) and B(2p + l) can be easily computed, where 1 <p<s,0<l<2, s<2p+l<2s.