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

Saira, Shuhuang Xiang and Guidong Liu
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Saira: School of Mathematics and Statistics, Central South University, Changsha 410083, China
Shuhuang Xiang: School of Mathematics and Statistics, Central South University, Changsha 410083, China
Guidong Liu: School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815, China

Mathematics, 2019, vol. 7, issue 10, 1-11

Abstract: 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.

Keywords: Clenshaw–Curtis–Filon; high oscillation; singular integral equations; boundary singularities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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