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

2006/11/26 by Van de Vyver, Hans
#65L05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.math/0611801

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.

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