Numerical solution of highly oscillatory nonlinear integrals using quasi-Monte Carlo methods

Abstract

Highly oscillating integrals occur in many engineering applications. This paper discusses the quasi-Monte Carlo methods for calculation of the highly oscillating integrals using a low discrepancy sequence. We evaluated the highly oscillating integrals using a low discrepancy sequence known as Vander Corput sequence. The theoretical error bounds are calculated and are compared with analytical results. The reliability of the quasi-Monte Carlo methods is compared with He’s homotopy perturbation method.