Indefinite integration of oscillatory functions by the Chebyshev series expansion

DOI10.1016/0377-0427(87)90035-5zbMath0613.65145OpenAlexW2085712018MaRDI QIDQ1819569

Takemitsu Hasegawa, Tatsuo Torii

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0377-0427(87)90035-5

zbMATH Keywords

Chebyshev series expansionautomatic quadraturethree term recurrenceindefinite integration of oscillatory functionoscillatory infinite integralSidi's extrapolation

Mathematics Subject Classification ID

Trigonometric interpolation (42A15) Approximate quadratures (41A55) Numerical methods for trigonometric approximation and interpolation (65T40) Numerical integration (65D30)

Related Items

DQAINF: An algorithm for automatic integration of infinite oscillating tails, Evaluating infinite integrals involving Bessel functions of arbitrary order, A comparison of some methods for the evaluation of highly oscillatory integrals, Application of a modified FFT to product type integration, The double exponential formula for oscillatory functions over the half infinite interval, A method for indefinite integration of oscillatory and singular functions, Computation of infinite integrals involving Bessel functions of arbitrary order by the \(\overline{D}\)-transformation, An Algorithm for Nondominant Solutions of Linear Second-Order Inhomogeneous Difference Equations, Approximating Cauchy-type singular integral by an automatic quadrature scheme, A user-friendly method for computing indefinite integrals of oscillatory functions, An automatic integration procedure for infinite range integrals involving oscillatory kernels, Computation of irregularly oscillating integrals

Uses Software

• QUADPACK

Cites Work

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• An algorithm for a special case of a generalization of the Richardson extrapolation process
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• Generalized Chebyshev Interpolation and Its Application to Automatic Quadrature
• Some Properties of a Generalization of the Richardson Extrapolation Process
• Extrapolation Methods for Oscillatory Infinite Integrals
• The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation
• Computational Aspects of Three-Term Recurrence Relations