Efficient quadrature for highly oscillatory integrals involving critical points

DOI10.1016/j.cam.2006.08.018zbMath1119.65019OpenAlexW2079157924MaRDI QIDQ2370682

Shuhuang Xiang

Publication date: 29 June 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.2006.08.018

zbMATH Keywords

numerical examplesquadratureGauss-Legendre quadratureoscillatory integralLevin collocation method

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40)

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Cites Work

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• A high order, progressive method for the evaluation of irregular oscillatory integrals
• A comparison of some methods for the evaluation of highly oscillatory integrals
• On quadrature methods for highly oscillatory integrals and their implementation
• Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
• Efficient quadrature of highly oscillatory integrals using derivatives
• Moment-free numerical integration of highly oscillatory functions