线性高振荡常微分方程两个数值解法的误差分析

Error Analysis of Two Numerical Methods for Linear Highly-Oscillatory Ordinary Differential Equations

以特殊的线性振荡方程y″+g(t)y=0(其中limt→∞g(t)=+∞)为例讨论了高振荡微分方程数值解问题.分析了梯形格式的整体截断误差,并对梯形格式做了修改,讨论了修改后格式的整体截断误差,使得整体截断误差中的T9/4变成了T-1/4.

This paper deals with numerical solution of highly oscillatory systems with a special reference to the linear oscillator y″ ＋ g （ t ） y = 0 （where limg t→∞ （ t ） = ＋ ∞ ）. We analysis the global error of trapezoidal method. Then we modify trapezoidal method and explore the global error of modified method and change the global error T^9/4 to T^-1/4.