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

Author

Listed:
  • SAIRA

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China
    Current address: School of Mathematics and Statistics, Central South University, Changsha 410083, China.)

  • Shuhuang Xiang

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China
    Current address: School of Mathematics and Statistics, Central South University, Changsha 410083, China.)

  • Guidong Liu

    (School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815, China)

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.

Suggested Citation

  • SAIRA & Shuhuang Xiang & Guidong Liu, 2019. "Numerical Solution of the Cauchy-Type Singular Integral Equation with a Highly Oscillatory Kernel Function," Mathematics, MDPI, vol. 7(10), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:872-:d:269133
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    References listed on IDEAS

    as
    1. Liu, Guidong & Xiang, Shuhuang, 2019. "Clenshaw–Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 251-267.
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    Cited by:

    1. SAIRA & Wen-Xiu Ma, 2022. "An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-16, October.

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