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Numerical analysis of a fast integration method for highly oscillatory functions

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Abstract

The integration of systems containing Bessel functions is a central point in many practical problems in physics, chemistry and engineering. This paper presents a new numerical analysis for the collocation method presented by Levin for \(\int_a^b f(x)S(rx)dx\) and gives more accurate error analysis about the integration of systems containing Bessel functions. The effectiveness and accuracy of the quadrature is tested for Bessel functions with large arguments.

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Authors and Affiliations

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

    Shuhuang Xiang

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  1. Shuhuang Xiang
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Correspondence to Shuhuang Xiang.

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AMS subject classification (2000)

65D32, 65D30

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Xiang, S. Numerical analysis of a fast integration method for highly oscillatory functions . Bit Numer Math 47, 469–482 (2007). https://doi.org/10.1007/s10543-007-0127-y

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  • DOI: https://doi.org/10.1007/s10543-007-0127-y

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