Numerical analysis of a fast integration method for highly oscillatory functions

The integration of systems containing Bessel functions is a central point in many practical problems in physics, chemistry and engineering. This paper presents a new numerical analysis for the collocation method presented by Levin for $\int_a^b f(x)S(rx)dx$ and gives more accurate error analysis about the integration of systems containing Bessel functions. The effectiveness and accuracy of the quadrature is tested for Bessel functions with large arguments.