A comparative study of Filon-type rules for oscillatory integrals

Hassan Majidian

doi:10.33993/jnaat531-1380

Authors

Hassan Majidian Department of Multidisciplinary Studies, Faculty of Encyclopedia Studies, Institute for Humanities and Cultural Studies, Tehran, Iran

DOI:

https://doi.org/10.33993/jnaat531-1380

Keywords:

oscillatory integral, Filon-Clenshaw-Curtis rule, extended FCC rule, adaptive FCC rule

Abstract views: 52

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).

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