Letter to the Editor: On the Filon and Levin methods for highly oscillatory integral

Authors:
Shuhuang Xiang
Affiliations:
Department of Mathematics, Central South University, Changsha, Hunan 410083, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 2
Cited 3

Fast integration of rapidly oscillatory functions

Journal of Computational and Applied Mathematics
Analysis of a collocation method for integrating rapidly oscillatory functions

Journal of Computational and Applied Mathematics

On the Levin iterative method for oscillatory integrals

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A parameter method for computing highly oscillatory integrals

Computers & Mathematics with Applications
Filon-Clenshaw-Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities

Journal of Computational and Applied Mathematics

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Abstract

This paper shows that for any suitably smooth function f(x) and arbitrarily selected interpolation nodes c1,c2,…,cv in [a,b], the Filon method and the Levin method for with the polynomial interpolation approach are identical when g(x) is a linear function. Based on this result, a new efficient Levin quadrature for is presented.