Numerische Mathematik

, Volume 105, Issue 4, pp 633–658

Efficient Filon-type methods for \(\int_a^bf(x)\,{\rm e}^{{\rm i}\omega g(x)}\,{\rm d}x\)


DOI: 10.1007/s00211-006-0051-0

Cite this article as:
Xiang, S. Numer. Math. (2007) 105: 633. doi:10.1007/s00211-006-0051-0


Based on the transformation y = g(x), some new efficient Filon-type methods for integration of highly oscillatory function \(\int_a^bf(x)\,{\rm e}^{{\rm i}\omega g(x)}\,{\rm d}x\) with an irregular oscillator are presented. One is a moment-free Filon-type method for the case that g(x) has no stationary points in [a,b]. The others are based on the Filon-type method or the asymptotic method together with Filon-type method for the case that g(x) has stationary points. The effectiveness and accuracy are tested by numerical examples.

AMS Subject Classifications

65D32 65D30 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Applied Mathematics and SoftwareCentral South UniversityChangshaChina