Evaluating infinite range oscillatory integrals using generalised quadrature methods

DOI10.1016/j.apnum.2005.12.003zbMath1105.65027OpenAlexW1966323586MaRDI QIDQ857026

N. E. Zubov

Publication date: 14 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2005.12.003

zbMATH Keywords

numerical examplesoscillatory integralsirregular oscillatory integralsinfinite range integralsgeneralised quadrature

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

On the calculation of highly oscillatory integrals with an algebraic singularity, Choice of specific interpolation points in quadrature formula for fast oscillating integrals, A short tale of long tail integration, Fast computation of singular oscillatory Fourier transforms, On numerical computation of integrals with integrands of the form \(f(x)\sin(w/x^r)\) on [0,1], Suitable Gauss and Filon-type methods for oscillatory integrals with an algebraic singularity, Efficient computation of highly oscillatory Fourier-type integrals with monomial phase functions and Jacobi-type singularities, Gauss-type quadrature for highly oscillatory integrals with algebraic singularities and applications, Efficient and accurate quadrature methods of Fourier integrals with a special oscillator and weak singularities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A high order, progressive method for the evaluation of irregular oscillatory integrals
• Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series
• Comparison of some methods for evaluating infinite range oscillatory integrals
• On computing uniformly valid approximations for viscous waves on a plane beach
• The evaluation of oscillatory integrals with infinite limits
• Some theoretical aspects of generalised quadrature methods.
• A method to generate generalized quadrature rules for oscillatory integrals
• Partition-extrapolation methods for numerical quadratures
• Theory of axially symmetric cusped focusing: numerical evaluation of a Bessoid integral by an adaptive contour algorithm
• The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation
• Development of non-linear transformations for improving convergence of sequences
• Some new thoughts on Gauss–Laguerre quadrature