On the Filon and Levin methods for highly oscillatory integral \(\smallint^{b}_{a}f(x)e^{iwg(x)}\,dx\)

DOI10.1016/j.cam.2006.10.006zbMath1129.65017OpenAlexW2274617172MaRDI QIDQ2381629

Shuhuang Xiang

Publication date: 18 September 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.10.006

zbMATH Keywords

quadratureoscillatory integralLevin methodFilon methodinterpolation nodes

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (15)

A well-conditioned Levin method for calculation of highly oscillatory integrals and its application ⋮ Filon-Clenshaw-Curtis formulas for highly oscillatory integrals in the presence of stationary points ⋮ Fast and stable augmented Levin methods for highly oscillatory and singular integrals ⋮ Filon-Clenshaw-Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities ⋮ Computing highly oscillatory integrals ⋮ On the evaluation of highly oscillatory integrals with high frequency ⋮ An improved algorithm for the evaluation of Cauchy principal value integrals of oscillatory functions and its application ⋮ On Filon methods for a class of Volterra integral equations with highly oscillatory Bessel kernels ⋮ Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral ⋮ Numerical approximation of oscillatory integrals of the linear ship wave theory ⋮ A parameter method for computing highly oscillatory integrals ⋮ A Gaussian quadrature rule for Fourier-type highly oscillatory integrals in the presence of stationary points ⋮ Efficient computation of highly oscillatory integrals with weak singularities by Gauss-type method ⋮ Levin methods for highly oscillatory integrals with singularities ⋮ Galerkin-Levin method for highly oscillatory integrals

Cites Work

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• Fast integration of rapidly oscillatory functions
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• Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
• On the numerical quadrature of highly-oscillating integrals II: Irregular oscillators
• On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
• Efficient quadrature of highly oscillatory integrals using derivatives

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