Next Article in Journal
Bivariate α,q-Bernstein–Kantorovich Operators and GBS Operators of Bivariate α,q-Bernstein–Kantorovich Type
Previous Article in Journal
Efficient Pipelined Broadcast with Monitoring Processing Node Status on a Multi-Core Processor
Previous Article in Special Issue
Extended Rectangular M-Metric Spaces and Fixed Point Results
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
Show Figures

Graphical abstract

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop