求解无阻尼Duffing方程的三角拟合显式对称六步法

摘要

本文利用多频三角拟合多步法求解无阻尼Duffing方程，构造包含不同共振谱的四种三角拟合对称六步法，分析新方法的稳定性和相性质。数值实验的结果显示新方法的有效性。%In this paper,a class of trigonometrically fitted explicit symmetric six-step methods for the numerical integration of undamped duffing equation is developed. Using multi-frequency trigonometrically fitted technique,we design four types of six-step methods which contain different resonance spectrum. Numerical stability and phase properties of the new methods are analyzed to explain the final numerical experiment.