A collocation method for high-frequency scattering by convex polygons
Journal of Computational and Applied Mathematics
Efficient evaluation of highly oscillatory acoustic scattering surface integrals
Journal of Computational and Applied Mathematics
On the Levin iterative method for oscillatory integrals
Journal of Computational and Applied Mathematics
Numerical quadrature for Bessel transformations
Applied Numerical Mathematics
An integration scheme for electromagnetic scattering using plane wave edge elements
Advances in Engineering Software
A parameter method for computing highly oscillatory integrals
Computers & Mathematics with Applications
On the evaluation of Cauchy principal value integrals of oscillatory functions
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Local solutions to high-frequency 2D scattering problems
Journal of Computational Physics
An improved Levin quadrature method for highly oscillatory integrals
Applied Numerical Mathematics
Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature
Journal of Approximation Theory
On the Fourier Extension of Nonperiodic Functions
SIAM Journal on Numerical Analysis
A rapid solution of a kind of 1D Fredholm oscillatory integral equation
Journal of Computational and Applied Mathematics
Numerical approximations to integrals with a highly oscillatory Bessel kernel
Applied Numerical Mathematics
Efficient quadrature of highly oscillatory integrals with algebraic singularities
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Computation of integrals with oscillatory and singular integrands using Chebyshev expansions
Journal of Computational and Applied Mathematics
Interpolatory Quadrature Rules for Oscillatory Integrals
Journal of Scientific Computing
Algorithm 935: IIPBF, a MATLAB toolbox for infinite integral of products of two Bessel functions
ACM Transactions on Mathematical Software (TOMS)
Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
Journal of Computational and Applied Mathematics
On evaluation of Bessel transforms with oscillatory and algebraic singular integrands
Journal of Computational and Applied Mathematics
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We consider the integration of one-dimensional highly oscillatory functions. Based on analytic continuation, rapidly converging quadrature rules are derived for a general class of oscillatory integrals with an analytic integrand. The accuracy of the quadrature increases both for the case of a fixed number of points and increasing frequency, and for the case of an increasing number of points and fixed frequency. These results are then used to obtain quadrature rules for more general oscillatory integrals, i.e., for functions that exhibit some smoothness but that are not analytic. The approach described in this paper is related to the steepest descent method, but it does not employ asymptotic expansions. It can be used for small or moderate frequencies as well as for very high frequencies. The approach is compared with the oscillatory integration techniques recently developed by Iserles and Norsett.