A comparative study of Filon-type rules for oscillatory integrals

Abstract

Our aim is to answer the following question: "Among the Filon-type methods for computing oscillatory integrals, which one is the most efficient in practice?". We first discuss why we should seek the answer among the family of Filon-Clenshaw-Curtis rules. A theoretical analysis accompanied by a set of numerical experiments reveals that the plain Filon-Clenshaw-Curtis rules reach a given accuracy faster than the (adaptive) extended Filon-Clenshaw-Curtis rules. The comparison is based on the CPU run-time for certain wave numbers (medium and large).