解周期初值问题的三角拟合两步方法

Trigonometrically fitted two-step method for periodic initial value problems

在很多由微分方程表征的应用系统中,经常面对有周期解微分方程的求解问题.由于微分方程周期解具有振荡特性,使得一些经典方法,如常系数数值等方法求解这类问题难以得到较好的结果.本文基于Adams-Bashforth经典方法,通过构造迭代方程,给出了求解具有周期初值问题的三角拟合法,并对该方法的稳定性进行了分析.数值试验表明,该方法可较好解决有周期解微分方程的求解问题.

ODEs with periodic solutions often appear in the application systems expressed by ODEs. Classical numerical methods with constant coefficients can not get perfect results when deal with these problems due to their oscillatory character. In this pa- per, we consider the trigonometrically fitted two - step method for the numerical integration of periodic initial value problems. This method is based on the original Adams - Bashforth method of order second. We analyzed the numerical stability of the new method. The numerical experiments are reported to show the efficiency and robustness of our new method.