On the computation of Fourier transforms of singular functions
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
A method to generate generalized quadrature rule for oscillatory integrals
Applied Numerical Mathematics
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
SIAM Journal on Numerical Analysis
Is Gauss Quadrature Better than Clenshaw-Curtis?
SIAM Review
Numerical Methods in Scientific Computing: Volume 1
Numerical Methods in Scientific Computing: Volume 1
On numerical computation of integrals with integrands of the form f(x)sin(w/xr) on [0, 1]
Journal of Computational and Applied Mathematics
Suitable Gauss and Filon-type methods for oscillatory integrals with an algebraic singularity
Applied Numerical Mathematics
A parameter method for computing highly oscillatory integrals
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
On the evaluation of Cauchy principal value integrals of oscillatory functions
Journal of Computational and Applied Mathematics
Error bounds for approximation in Chebyshev points
Numerische Mathematik
Journal of Computational and Applied Mathematics
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In this paper we are concerned with the numerical evaluation of a class of highly oscillatory integrals containing algebraic singularities. First, we expand such integrals derived by two transformations t=x^-^@b,@b0,t=21+z,-1@?z@?1, into asymptotic series in inverse powers of the frequency @w. Then, based the asymptotic series, two methods are presented. One is the Filon-type method. The other is the Clenshaw-Curtis-Filon-type method which is based on a special Hermite interpolation polynomial in the Clenshaw-Curtis points and can be evaluated efficiently in O(NlogN) operations, where N+1 is the number of Clenshaw-Curtis points in the interval of integration. Some error and convergence analysis and robust numerical examples are used to demonstrate the accuracy and effectiveness of the proposed approaches for approximating the class of highly oscillatory singular integrals.