A mono-implicit Runge-Kutta-Nystrom modification of the Numerov method

[摘要] We present two two-parameter families of fourth-order mono-implicit Runge-Kutta-Nystrom methods. Each member of these families can be considered as a modification of the Numerov method. We analyze the stability and periodicity properties of these methods. It is shown that (i) within one of these families there exist A-stable (even L-stable) and P-stable methods, and (ii) in both families there exist methods with a phase lag of order six.

[发布日期] 1997-02-03

[关键词] second-order ODEs;Runge-Kutta-Nystrom methods;mono-implicit methods;stability;periodicity;phase lag