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Open AccessFeature PaperArticle

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

1
Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
2
Department of Electrical Engineering, University of Engineering and Technology, Peshawar 25000, Pakistan
3
Department of Electronics Engineering, Hankuk University of Foreign Studies, Yongin 17035, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1160; https://doi.org/10.3390/math7121160
Received: 30 October 2019 / Revised: 21 November 2019 / Accepted: 21 November 2019 / Published: 2 December 2019
(This article belongs to the Special Issue Applications in Theoretical and Computational Fixed Point Problems)
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. View Full-Text
Keywords: Chebyshev–Levin quadrature; adaptive splitting algorithm; multi-resolution quadratures; Chebyshev differentiation matrix Chebyshev–Levin quadrature; adaptive splitting algorithm; multi-resolution quadratures; Chebyshev differentiation matrix
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MDPI and ACS Style

Zaman, S.; Hussain, I.; Singh, D. Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point. Mathematics 2019, 7, 1160. https://doi.org/10.3390/math7121160

AMA Style

Zaman S, Hussain I, Singh D. Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point. Mathematics. 2019; 7(12):1160. https://doi.org/10.3390/math7121160

Chicago/Turabian Style

Zaman, Sakhi; Hussain, Irshad; Singh, Dhananjay. 2019. "Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point" Mathematics 7, no. 12: 1160. https://doi.org/10.3390/math7121160

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