Analysis of a collocation method for integrating rapidly oscillatory functions

A collocation method for approximating integrals of rapidly oscillatory functions is analyzed. The method is efficient for integrals involving Bessel functions Jv(rx) with a large oscillation frequency parameter r, as well as for many other one- and multi-dimensional integrals of functions with rapid irregular oscillations. The analysis provides a convergence rate and it shows that the relative error of the method is even decreasing as the frequency of the oscillations increases.