The Numerical Evaluation of Very Oscillatory Infinite Integrals by Extrapolation
From MaRDI portal
Publication:4746725
DOI10.2307/2007286zbMath0508.65011OpenAlexW4248939144MaRDI QIDQ4746725
Publication date: 1982
Full work available at URL: https://doi.org/10.2307/2007286
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Extrapolation to the limit, deferred corrections (65B05) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)
Related Items
DQAINF: An algorithm for automatic integration of infinite oscillating tails ⋮ Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability ⋮ The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature ⋮ Evaluating infinite range oscillatory integrals using generalised quadrature methods ⋮ Transient response of a thermoelastic half-space to mechanical and thermal buried sources ⋮ Evaluating infinite integrals involving Bessel functions of arbitrary order ⋮ Mahler measures, short walks and log-sine integrals ⋮ Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems ⋮ A short tale of long tail integration ⋮ Application of the W-transformation to compute the linearised 2-d beach problem potentials ⋮ A note on an extension of extrapolative techniques for a class of infinite oscillatory integrals ⋮ High-precision computation: mathematical physics and dynamics ⋮ Molecular integrals for Slater type orbitals using Coulomb Sturmians ⋮ Computation of infinite integrals involving Bessel functions of arbitrary order by the \(\overline{D}\)-transformation ⋮ 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 ⋮ Summability experiments with a class of divergent inverse Kontorovich-Lebedev transforms ⋮ Asymptotic analysis of a generalized Richardson extrapolation process on linear sequences ⋮ A User-Friendly Extrapolation Method for Oscillatory Infinite Integrals ⋮ On rates of acceleration of extrapolation methods for oscillatory infinite integrals ⋮ A numerical evaluation of very oscillatory infinite integrals by asymptotics ⋮ Indefinite integration of oscillatory functions by the Chebyshev series expansion ⋮ An automatic integration procedure for infinite range integrals involving oscillatory kernels ⋮ Computation of irregularly oscillating integrals ⋮ Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function ⋮ Efficient and rapid numerical evaluation of the two-electron, four-center Coulomb integrals using nonlinear transformations and useful properties of sine and Bessel functions ⋮ High-precision arithmetic in mathematical physics