An efficient method for evaluating the integral of a class of highly oscillatory functions

Highly oscillatory integrals require special techniques for their effective evaluation. Various studies have been conducted to find computational methods for evaluating such integrals. In this paper we present an efficient numerical method to evaluate a class of generalised Fourier integrals (on a line or a square) with integrands of the form f(x)eikg(x), under the assumption that in the domain of integration, both ff and gg are sufficiently smooth and that gg does not have any stationary/critical points. Numerical analysis and results are given to illustrate the effectiveness of our method for computing generalised Fourier integrals.