关于求解二阶周期性初值问题具有极小相位延迟的P—稳定的Hybrid方法

P-STABLE HYBRID METHOD WITH MINIMAL PHASE-LAG FOR SECOND ORDER PERIODIC INITIAL VALUE PROBLEMS

本文提出了一类求解二阶周期性初值问题y"=f(x,y)的具有极小相位延迟的P—稳定的Hybrid方法。其精度与相位延迟的阶均比[1～3]中的同类方法高。本文10阶方法M_(10)(β)只须求f的二阶全导数,6阶方法M_6(β)及8阶方法M_8(β,γ)不需求f的全导数。数值结果表明,本文所构造的方法是有效的。

In this paper, we put forward a class of two-step high order P-stable methods with minimal phase-lag for the numerical intergration of second order periodic initial value problems. These methods have the advantage of higher accuracy and smaller phase-lag compared with the P-stable methods in (1)-(3). Numerical example showed these methods here to be efficient.