A rapid solution of a kind of 1D Fredholm oscillatory integral equation

DOI10.1016/j.cam.2012.01.007zbMath1243.65162OpenAlexW2042617956MaRDI QIDQ408210

Shunping Xiao, Tao Wang, Jianbing Li, Xue-Song Wang

Publication date: 29 March 2012

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.2012.01.007

zbMATH Keywords

spectral methodbarycentric interpolationChebyshev differentiation matrixLevin methodoscillatory integral equationstationary phase point

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20)

Related Items (13)

Meshless procedure for highly oscillatory kernel based one-dimensional Volterra integral equations ⋮ A collocation method for a class of Fredholm integral equations with highly oscillatory kernels ⋮ Meshless methods for multivariate highly oscillatory Fredholm integral equations ⋮ High asymptotic order methods for highly oscillatory integral equations with trigonometric kernels ⋮ Error estimates of piecewise Hermite collocation method for highly oscillatory Volterra integral equation with Bessel kernel ⋮ Meshless methods for one-dimensional oscillatory Fredholm integral equations ⋮ The generalized quadrature method for a class of highly oscillatory Volterra integral equations ⋮ Meshless methods for two-dimensional oscillatory Fredholm integral equations ⋮ Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels ⋮ A Chebyshev collocation method for a class of Fredholm integral equations with highly oscillatory kernels ⋮ Efficient collocation methods for Volterra integral equations with highly oscillatory kernel ⋮ Meshless approximation method of one-dimensional oscillatory Fredholm integral equations ⋮ On fast multipole methods for Fredholm integral equations of the second kind with singular and highly oscillatory kernels

Uses Software

• Matlab

Cites Work

• Evaluation of Cauchy principal value integrals of oscillatory kind
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• A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering Problems
• Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
• The Numerical Solution of Integral Equations of the Second Kind
• Spectral Methods in MATLAB
• Barycentric Lagrange Interpolation
• Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: the convex case
• Efficient quadrature of highly oscillatory integrals using derivatives
• Moment-free numerical integration of highly oscillatory functions
• Integral Equations with a Rapidly Oscillating Kernel
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