Phase properties of exponentially-fitted symmetric multistep methods for y''=f(x,y)

Details Phase properties of exponentially-fitted symmetric multistep methods for y''=f(x,y) Phase properties of exponentially-fitted symmetric multistep methods for y''=f(x,y)

2006-11-26

arxiv.org/abs/math/0611801v1

Mathematics

Numerical Analysis

Scientific paper

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.

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