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An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations

Author

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  • SAIRA

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    Department of Mathematics, Government College University, Lahore 54000, Pakistan
    School of Mathematics and Statistics, Central South University, Changsha 410083, China)

  • Wen-Xiu Ma

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
    School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa)

Abstract

This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate the singular integral, the unknown function approximated by an interpolation polynomial is rewritten as a Taylor series expansion. A system of linear equations of FIDEs obtained by using equally spaced points as collocation points is solved to obtain the unknown function. The proposed method attains higher accuracy rates, which are proven by error analysis and some numerical examples as well.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3628-:d:933553
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Rohaninasab, N. & Maleknejad, K. & Ezzati, R., 2018. "Numerical solution of high-order Volterra–Fredholm integro-differential equations by using Legendre collocation method," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 171-188.
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