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Numerical Solution of the Cauchy-Type Singular Integral Equation with a Highly Oscillatory Kernel Function

by SAIRA 1,†, Shuhuang Xiang 1,*,† and Guidong Liu 2
1
School of Mathematics and Statistics, Central South University, Changsha 410083, China
2
School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815, China
*
Author to whom correspondence should be addressed.
Current address: School of Mathematics and Statistics, Central South University, Changsha 410083, China.
Mathematics 2019, 7(10), 872; https://doi.org/10.3390/math7100872
Received: 16 August 2019 / Revised: 17 September 2019 / Accepted: 18 September 2019 / Published: 20 September 2019
This paper aims to present a Clenshaw–Curtis–Filon quadrature to approximate the
solution of various cases of Cauchy-type singular integral equations (CSIEs) of the second kind with
a highly oscillatory kernel function. We adduce that the zero case oscillation (k = 0) proposed method
gives more accurate results than the scheme introduced in Dezhbord at el. (2016) and Eshkuvatov
at el. (2009) for small values of N. Finally, this paper illustrates some error analyses and numerical
results for CSIEs. View Full-Text
Keywords: Clenshaw–Curtis–Filon; high oscillation; singular integral equations; boundary singularities Clenshaw–Curtis–Filon; high oscillation; singular integral equations; boundary singularities
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SAIRA; Xiang, S.; Liu, G. Numerical Solution of the Cauchy-Type Singular Integral Equation with a Highly Oscillatory Kernel Function. Mathematics 2019, 7, 872.

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