An improved Levin quadrature method for highly oscillatory integrals

DOI10.1016/j.apnum.2010.04.009zbMath1190.65040OpenAlexW2026526254MaRDI QIDQ979225

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

Publication date: 25 June 2010

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2010.04.009

zbMATH Keywords

ordinary differential equationill-conditioned matrixspectral methodtruncated singular value decompositionoscillatory integralChebyshev differentiation matrixLevin method

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32)

Related Items (15)

A comparative study of meshless complex quadrature rules for highly oscillatory integrals ⋮ Numerical Integration of Highly Oscillating Functions ⋮ An adaptive Filon-type method for oscillatory integrals without stationary points ⋮ Evaluation of Cauchy principal value integrals of oscillatory kind ⋮ Phase function methods for second order inhomogeneous linear ordinary differential equations ⋮ On the evaluation of highly oscillatory integrals with high frequency ⋮ Meshless and wavelets based complex quadrature of highly oscillatory integrals and the integrals with stationary points ⋮ New quadrature rules for highly oscillatory integrals with stationary points ⋮ A well-conditioned and efficient Levin method for highly oscillatory integrals with compactly supported radial basis functions ⋮ Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral ⋮ Numerical approximation of oscillatory integrals of the linear ship wave theory ⋮ On an improved-Levin oscillatory quadrature method ⋮ Numerical integration of multi-dimensional highly oscillatory integrals, based on eRPIM ⋮ Efficient computation of highly oscillatory Fourier-type integrals with monomial phase functions and Jacobi-type singularities ⋮ Numerical methods for multivariate highly oscillatory integrals

Uses Software

• Matlab
• Regularization tools
• UTV

Cites Work

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• Analysis of the radar reflectivity of aircraft vortex wakes
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• Quadrature methods for multivariate highly oscillatory integrals using derivatives
• A Simple "Filon-Trapezoidal" Rule

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