SYMPLECTIC RK METHODS AND SYMPLECTIC PRK METHODS WITH REAL EIGENVALUES

• 来源期刊: 计算数学（英文版）
• 关键词: Runge-Kutta method Partitioned Runge-Kutta method Symplectic Real eigenvalues.
• 年，卷（期）: 2004,（5）
• 页码范围: 769-776
• 页数: 8页
• 语种: 英文

摘要

Properties of symplectic Runge-Kutta (RK) methods and symplectic partitioned RungeKutta (PRK) methods with real eigenvalues are discussed in this paper. It is shown that an s stage such method can't reach order more than s + 1. Particularly, we prove that no symplectic RK method with real eigenvalues exists in stage s of order s + 1 when s is even. But an example constructed by using the W-transformation shows that PRK method of this type does not necessarily meet this order barrier. Another useful way other than W-transformation to construct symplectic PRK method with real eigenvalues is then presented. Finally, a class of efficient symplectic methods is recommended.