Fast computation of integrals with fourier-type oscillator involving stationary point

Abstract

An adaptive splitting algorithm was implemented for numerical evaluation of Fourier-type highly oscillatory integrals involving stationary point. Accordingly, a modified Levin collocation method was coupled with multi-resolution quadratures in order to tackle the stationary point and irregular oscillations of the integrand caused by ω. Some test problems are included to verify the accuracy of the proposed methods.