Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point

Sakhi Zaman, Irshad Hussain and Dhananjay Singh
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Sakhi Zaman: Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
Irshad Hussain: Department of Electrical Engineering, University of Engineering and Technology, Peshawar 25000, Pakistan
Dhananjay Singh: Department of Electronics Engineering, Hankuk University of Foreign Studies, Yongin 17035, Korea

Mathematics, 2019, vol. 7, issue 12, 1-14

Abstract: An adaptive splitting algorithm was implemented for numerical evaluation of Fourier-type highly oscillatory integrals involving stationary point. Accordingly, a modified Levin collocation method was coupled with multi-resolution quadratures in order to tackle the stationary point and irregular oscillations of the integrand caused by ω . Some test problems are included to verify the accuracy of the proposed methods.

Keywords: Chebyshev–Levin quadrature; adaptive splitting algorithm; multi-resolution quadratures; Chebyshev differentiation matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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