The exponential accuracy of Fourier and Chebyshev differencing methods
SIAM Journal on Numerical Analysis
Analysis of a collocation method for integrating rapidly oscillatory functions
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
SIAM Journal on Numerical Analysis
Letter to the Editor: On the Filon and Levin methods for highly oscillatory integral
Journal of Computational and Applied Mathematics
A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering Problems
SIAM Journal on Scientific Computing
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
Shifted GMRES for oscillatory integrals
Numerische Mathematik
On the convergence of Filon quadrature
Journal of Computational and Applied Mathematics
Efficient quadrature of highly oscillatory integrals with algebraic singularities
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
Hi-index | 7.29 |
In this work we propose and analyse a numerical method for computing a family of highly oscillatory integrals with logarithmic singularities. For these quadrature rules we derive error estimates in terms of N, the number of nodes, k the rate of oscillations and a Sobolev-like regularity of the function. We prove that the method is not only robust but the error even decreases, for fixed N, as k increases. Practical issues about the implementation of the rule are also covered in this paper by: (a) writing down ready-to-implement algorithms; (b) analysing the numerical stability of the computations and (c) estimating the overall computational cost. We finish by showing some numerical experiments which illustrate the theoretical results presented in this paper.