On efficient computation of highly oscillatory retarded potential integral equations. Issue 11 (2nd November 2018)

• Record Type: Journal Article
• Authors: Xiang, Shuhuang; Li, Bin; Liu, Guidong
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 11(2018)
• Page Start: 2240
• Page End: 2255
• Publication Date: 2018-11-02
• Subjects: Retarded potential integral equations -- spatially time-harmonic incident wave -- Bessel function -- highly oscillatory Volterra integral equations -- Clenshaw–Curtis-type method; 65D32 -- 65R20; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1380192
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: This paper presents an efficient numerical method for retarded potential integral equations with highly oscillatory spatially time-harmonic incident waves, which is based on inverse Fourier transforms and efficient algorithms for the highly oscillatory Volterra integral equation of the first kind. From the integral equation, it leads to an efficient approximation by applying the Clenshaw–Curtis-type method which costs the same operations independent of large values of frequencies. Applying inverse Fourier transforms yields numerical results on solving the retarded potential integral equations. Preliminary numerical results show the efficiency and accuracy of the approximations.