On the Levin iterative method for oscillatory integrals
Journal of Computational and Applied Mathematics
Numerical quadrature for Bessel transformations
Applied Numerical Mathematics
Suitable Gauss and Filon-type methods for oscillatory integrals with an algebraic singularity
Applied Numerical Mathematics
Numerical Quadrature for Bessel Transformations with High Oscillations
Numerical Analysis and Its Applications
A parameter method for computing highly oscillatory integrals
Computers & Mathematics with Applications
Efficient quadrature of highly oscillatory integrals with algebraic singularities
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Computation of integrals with oscillatory and singular integrands using Chebyshev expansions
Journal of Computational and Applied Mathematics
Fast Integration for Cauchy Principal Value Integrals of Oscillatory Kind
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Journal of Computational and Applied Mathematics
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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Based on the transformation y = g(x), some new efficient Filon-type methods for integration of highly oscillatory function $$\int_a^bf(x)\,{\rm e}^{{\rm i}\omega g(x)}\,{\rm d}x$$ with an irregular oscillator are presented. One is a moment-free Filon-type method for the case that g(x) has no stationary points in [a,b]. The others are based on the Filon-type method or the asymptotic method together with Filon-type method for the case that g(x) has stationary points. The effectiveness and accuracy are tested by numerical examples.