Gauss-type quadrature for highly oscillatory integrals with algebraic singularities and applications
DOI10.1080/00207160.2016.1184259zbMath1371.65024OpenAlexW2343756292MaRDI QIDQ4976311
Publication date: 28 July 2017
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160.2016.1184259
numerical examplediscontinuous Galerkin methodhighly oscillatory integralGauss-type quadratureasymptotic error estimateVolterra integral equation with highly oscillatory kernel
Numerical methods for integral equations (65R20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Volterra integral equations (45D05)
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- Efficient quadrature of highly oscillatory integrals with algebraic singularities
- Asymptotic analysis of numerical steepest descent with path approximations
- Analysis of a collocation method for integrating rapidly oscillatory functions
- Evaluating infinite range oscillatory integrals using generalised quadrature methods
- Efficient Filon-type methods for \(\int_a^b f(x)\,e^{i\omega g(x)}\, dx\)
- Numerical solutions to Volterra integral equations of the second kind with oscillatory trigonometric kernels
- Complex Gaussian quadrature of oscillatory integrals
- Numerical evaluation of a fixed-amplitude variable-phase integral
- Product integration rules for Volterra integral equations of the first kind
- A method to generate generalized quadrature rules for oscillatory integrals
- A perspective on the numerical treatment of Volterra equations
- Computation of integrals with oscillatory and singular integrands using Chebyshev expansions
- On evaluation of Bessel transforms with oscillatory and algebraic singular integrands
- On the implementation of discontinuous Galerkin methods for Volterra integral equations with highly oscillatory Bessel kernels
- Asymptotic expansions for oscillatory integrals using inverse functions
- Fast computation of a class of highly oscillatory integrals
- Asymptotic Representations of Fourier Integrals and the Method of Stationary Phase
- On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
- Discontinuous Galerkin approximations for Volterra integral equations of the first kind
- On the numerical evaluation of singular integrals
- Collocation Methods for Volterra Integral and Related Functional Differential Equations
- A Galerkin Boundary Element Method for High Frequency Scattering by Convex Polygons
- Efficient quadrature of highly oscillatory integrals using derivatives
- Moment-free numerical integration of highly oscillatory functions
- A Modification of Filon's Method of Numerical Integration
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