rungekuttanystrm方法的若干新性質(zhì)與階結(jié)果

1、湘潭大學(xué)碩士學(xué)位論文Runge-Kutta-Nystr ② if Φ is symmetric, then N Φis symmetric; ③ the simplifying assumptions of N Φgenerated from Φ can be droved; ④ * N Φ is symplectic when N Φis symplectic; ⑤ N Φand * N Φ have the

2、 same P-stability. By ① and ②, we provide a new approach to construct symplectic (or symmetric) RKN methods from symplectic (or symmetric) RK methods. (2) We investigate the order conditions and the order characterizat

3、ions of symplectic RKN methods and study the order of singly diagonally symplectic RKN methods and explicit RKN methods, and prove that the highest possible order is six. (3) Some examples of the symplectic RKN methods

4、are given from the symplectic RK methods. By using these examples, some numerical tests are presented. Key Words: Hamiltonian systems； Runge Kutta ?methods； Runge Kutta Nystrom ? ? ?? methods；Symplecticity；Adjoint meth