A high order, progressive method for the evaluation of irregular oscillatory integrals
Applied Numerical Mathematics
Stability and Convergence of Collocation Schemes for Retarded Potential Integral Equations
SIAM Journal on Numerical Analysis
A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
SIAM Journal on Scientific Computing
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
SIAM Journal on Numerical Analysis
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
Letter to the Editor: On quadrature of Bessel transformations
Journal of Computational and Applied Mathematics
Numerical approximations to integrals with a highly oscillatory Bessel kernel
Applied Numerical Mathematics
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In this paper, we study efficient methods for computing the integrals of the form @!"0^1x^a(1-x)^bf(x)J"v(@wx)dx, where a,b,v,@w are the given constants and @w@?1, J"v is the Bessel function of the first kind and of order v, f is a sufficiently smooth function on [0,1]. Firstly, we express the moments in a closed form with the aid of special functions. Secondly, we induce the Filon-type method based on the Taylor interpolation polynomial at two endpoints and the Hermite interpolation polynomial at Clenshaw-Curtis points on evaluating the highly oscillatory Bessel integrals with algebraic singularity. Theoretical results and numerical experiments perform that the methods are very efficient in obtaining very high precision approximations if @w is sufficiently large.