一类高振荡常微分方程数值解法的误差分析

The error analysis of numerical methods for a kind of 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的问题.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局部截断误差对整体截断误差的影响,最后给出了数值结果.

This paper deals with numerical solutions of highly-oscillatory ordinary differential equations with a special reference to the linear oscillator y″ ＋ g （ t ） y = 0 （ where limt→ ∞ （ t ） = ∞ ）. Analyzing＇ the global error, we modified the trapezoidal method. We investigated the influence of the modified local error on the global error. Finally, modified some numerical results were given.