Integration of Highly Oscillating Functions Using Prony Interpolation

Abstract

In this work we present an alternative way of integrating highly oscillating functions, using Prony interpolation (PI) technique. Such integrals appear in various engineering problems, including physical optics, high-frequency scattering, or retarded potential computations. We develop a quadrature for the numerical integration over a finite domain [a, b]. Domain [a, b] is suitably divided into subdomains, within each PI is performed on the integrand function. We investigate lower as well as higher order Prony interpolation (HOPI) schemes for the accurate computation of the integral. We compare HOPI quadrature in terms of function evaluations versus other suitable quadratures for highly oscillating functions, such as Matlab's quadgk, and we compare its accuracy with Levin type method. Various numerical results are presented.