On the numerical solution of second order differential equations in the high-frequency regime
Numerical Analysis
2015-06-23 v2
Abstract
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the 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 the performance of the method with several numerical experiments.
Keywords
Cite
@article{arxiv.1409.6049,
title = {On the numerical solution of second order differential equations in the high-frequency regime},
author = {James Bremer},
journal= {arXiv preprint arXiv:1409.6049},
year = {2015}
}