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BIT Numerical Mathematics

, Volume 47, Issue 2, pp 469–482 | Cite as

Numerical analysis of a fast integration method for highly oscillatory functions

  • Shuhuang Xiang
Article

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.

Key words

oscillatory integrals Bessel function error bounds collocation method 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Applied Mathematics and SoftwareCentral South UniversityChangshaP.R. China

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