Application of a modified FFT to product type integration

DOI10.1016/0377-0427(91)90168-JzbMath0754.65023MaRDI QIDQ1184119

Tatsuo Torii, Takemitsu Hasegawa

Publication date: 28 June 1992

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

zbMATH Keywords

singular integralrecurrence relationrecursionChebyshev polynomialsingular kernelsNumerical examplesautomatic integrationindefinite integralautomatic quadraturemodified fast Fourier transformproduct type integration

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Related Items (12)

Quadrature rule for indefinite integral of algebraic-logarithmic singular integrands ⋮ A pseudo-spectral method for a non-local KdV-Burgers equation posed on \(\mathbb{R}\) ⋮ Numerical integration of functions with poles near the interval of integration ⋮ A practical algorithm for computing Cauchy principal value integrals of oscillatory functions ⋮ A method for indefinite integration of oscillatory and singular functions ⋮ Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives ⋮ The numerical evaluation of two integral transforms ⋮ On the convergence of the method for indefinite integration of oscillatory and singular functions ⋮ Approximating Cauchy-type singular integral by an automatic quadrature scheme ⋮ Approximating the singular integrals of Cauchy type with weight function on the interval ⋮ Discretized Fractional Calculus with a Series of Chebyshev Polynomial ⋮ An automatic integration procedure for infinite range integrals involving oscillatory kernels

Uses Software

• QUADPACK

Cites Work

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• Error Bounds for Gaussian Quadrature of Analytic Functions
• Newton Interpolation in Fejer and Chebyshev Points
• Properties of Interpolatory Product Integration Rules
• Product-integration rules and their convergence
• An Algorithm Based on the FFT for a Generalized Chebyshev Interpolation
• Generalized Noninterpolatory Rules for Cauchy Principal Value Integrals
• An Automatic Quadrature for Cauchy Principal Value Integrals
• Truncation Errors in Two Chebyshev Series Approximations
• Implementing Clenshaw-Curtis quadrature, I methodology and experience

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