Indefinite integration of oscillatory functions by the Chebyshev series expansion
Journal of Computational and Applied Mathematics - Numerical Quadrature
Application of a modified FFT to product type integration
ISCM '90 Proceedings of the International Symposium on Computation mathematics
On the computation of Fourier transforms of singular functions
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
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 for Special Functions
Numerical Methods for Special Functions
Numerical Methods in Scientific Computing: Volume 1
Numerical Methods in Scientific Computing: Volume 1
A parameter method for computing highly oscillatory integrals
Computers & Mathematics with Applications
Error bounds for approximation in Chebyshev points
Numerische Mathematik
Hi-index | 7.29 |
We present a general method for computing oscillatory integrals of the form @!"-"1^1f(x)G(x)e^i^@w^xdx, where f is sufficiently smooth on [-1,1], @w is a positive parameter and G is a product of singular factors of algebraic or logarithmic type. Based on a Chebyshev expansion of f and the properties of Chebyshev polynomials, the proposed method for such integrals is constructed with the help of the expansion of the oscillatory factor e^i^@w^x. Furthermore, due to numerically stable recurrence relations for the modified moments, the devised scheme can be employed to compute oscillatory integrals with algebraic or logarithmic singularities at the end or interior points of the interval of integration. Numerical examples are provided to confirm our analysis.