Two robust methods for irregular oscillatory integrals over a finite range

DOI10.1016/0168-9274(94)00003-4zbMath0808.65012OpenAlexW2044406050MaRDI QIDQ1330475

Gwynne Evans

Publication date: 16 March 1995

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(94)00003-4

zbMATH Keywords

numerical exampleserror boundsFourier-type integralsoscillatory integralsintegration rulestrapezoidal and Simpson rules

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

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Numerical Integration of Highly Oscillating Functions ⋮ Efficient Filon method for oscillatory integrals ⋮ On the evaluation of highly oscillatory integrals with high frequency ⋮ Using B-spline frames to represent solutions of acoustics scattering problems ⋮ A comparison of some methods for the evaluation of highly oscillatory integrals ⋮ A high order, progressive method for the evaluation of irregular oscillatory integrals ⋮ A note on a recent study of oscillatory integration rules ⋮ Exponentially fitted quadrature rules of Gauss type for oscillatory integrands ⋮ An expansion method for irregular oscillatory integrals ⋮ Computation of irregularly oscillating integrals

Cites Work

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• Far Field Asymptotics of the Two-Dimensional Linearised Sloping Beach Problem
• Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
• Automatic generation of quadrature formulae for oscillatory integrals
• Numerical Evaluation of Fourier Integrals
• The use of Chebyshev series for the evaluation of oscillatory integrals

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