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

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Abstract

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.

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  1. Department of Applied Mathematics and Software, Central South University, Changsha, Hunan, 410083, China

    Shuhuang Xiang

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  1. Shuhuang Xiang
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Correspondence to Shuhuang Xiang.

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The Project-sponsored by SRF for ROCS, SEM, China and by JSPS Long-Term Invitation Fellowship Research Program, Japan.

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Xiang, S. Efficient Filon-type methods for \(\int_a^bf(x)\,{\rm e}^{{\rm i}\omega g(x)}\,{\rm d}x\) . Numer. Math. 105, 633–658 (2007). https://doi.org/10.1007/s00211-006-0051-0

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  • DOI: https://doi.org/10.1007/s00211-006-0051-0

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