Phase properties of exponentially-fitted symmetric multistep methods for y''=f(x,y)
Numerical Analysis
2007-05-23 v1
Abstract
A convenient tool to obtain numerical methods specially tuned on oscillating functions is exponential fitting. Such methods are needed in various branches of natural sciences, particularly in physics, since a lot of physical phenomena exhibit a pronounced oscillatory behavior. Many exponentially-fitted (EF) symmetric multistep methods for y''=f(x,y) are already developed. To have an idea of the accuracy we examine their phase properties. The remarkably simple expression of the phase-lag error obtained in Theorem 2 allows to draw quantitative conclusions on the merits of each EF version.
Keywords
Cite
@article{arxiv.math/0611801,
title = {Phase properties of exponentially-fitted symmetric multistep methods for y''=f(x,y)},
author = {Hans Van de Vyver},
journal= {arXiv preprint arXiv:math/0611801},
year = {2007}
}