On the numerical solution of second order ordinary differential equations in the high-frequency regime
On the numerical solution of second order ordinary differential equations in the high-frequency regime
复制标题
高频域二阶常微分方程的数值解
DOI：
10.1016/j.acha.2016.05.002
复制
发表时间：
2018
影响因子：
2.5
通讯作者：
Bremer, James
中科院分区：
文献类型：
--
作者：
Bremer, James
我们描述了一个算法的数值解的二阶线性常微分方程的高频政权。它是基于最近的观察，这种类型的方程的解决方案，可以准确地表示使用非振荡相函数。与常微分方程的标准求解器不同，我们的算法的运行时间与解的振荡频率无关。我们用几个数值实验说明了该方法的这一点和其他性质。
We describe an algorithm for the numerical solution of second order linear ordinary differential equations in the high-frequency regime. It is based on the recent observation that solutions of equations of this type can be accurately represented using nonoscillatory phase functions. Unlike standard solvers for ordinary differential equations, the running time of our algorithm is independent of the frequency of oscillation of the solutions. We illustrate this and other properties of the method with several numerical experiments.