Fast integration of rapidly oscillatory functions
Journal of Computational and Applied Mathematics
A high order, progressive method for the evaluation of irregular oscillatory integrals
Applied Numerical Mathematics
Analysis of a collocation method for integrating rapidly oscillatory functions
Journal of Computational and Applied Mathematics
A method to generate generalized quadrature rule for oscillatory integrals
Applied Numerical Mathematics
Homotopy perturbation method: a new nonlinear analytical technique
Applied Mathematics and Computation
Some theoretical aspects of generalised quadrature methods
Journal of Complexity
Stability and Convergence of Collocation Schemes for Retarded Potential Integral Equations
SIAM Journal on Numerical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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
Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval
Journal of Computational and Applied Mathematics
Efficient evaluation of oscillatory Bessel Hilbert transforms
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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In this paper, we consider a new numerical method for computing highly oscillatory Bessel transforms. We begin our analysis by using the integral form of Bessel function and its analytic continuation. Then we transform the integrals into the forms on [0,+~) that the integrand does not oscillate and decays exponentially fast, which can be efficiently computed by using Gauss-Laguerre quadrature rule. Moreover, we derive corresponding error bounds in terms of the frequency r and the point number n. Numerical examples based on theoretical results are presented to demonstrate the efficiency and accuracy of the proposed method.