An improved Levin quadrature method for highly oscillatory integrals

Authors:
Jianbing Li;Xuesong Wang;Tao Wang;Shunping Xiao
Affiliations:
College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China;College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China;College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China;College of Electronic Science and Engineering, National University of Defense Technology, Changsha 410073, China
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

How to calculate highly oscillatory integrals rapidly and accurately is one of the key problems in many fields. In this paper, an oscillatory quadrature algorithm based on Levin method is put forward. This method has a high computational speed and has addressed the problem that the Levin method is susceptible to the ill conditioning. Numerical experiments confirm the benefits of this method.