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Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay

Author

Listed:
  • Li Zhang

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Jin Huang

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Hu Li

    (School of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Yifei Wang

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

This paper proposes an extrapolation method to solve a class of non-linear weakly singular kernel Volterra integral equations with vanishing delay. After the existence and uniqueness of the solution to the original equation are proved, we combine an improved trapezoidal quadrature formula with an interpolation technique to obtain an approximate equation, and then we enhance the error accuracy of the approximate solution using the Richardson extrapolation, on the basis of the asymptotic error expansion. Simultaneously, a posteriori error estimate for the method is derived. Some illustrative examples demonstrating the efficiency of the method are given.

Suggested Citation

  • Li Zhang & Jin Huang & Hu Li & Yifei Wang, 2021. "Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1856-:d:609147
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    References listed on IDEAS

    as
    1. Ming, Wanyuan & Huang, Chengming & Zhao, Longbin, 2018. "Optimal superconvergence results for Volterra functional integral equations with proportional vanishing delays," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 292-301.
    2. Mosleh, Maryam & Otadi, Mahmood, 2015. "Least squares approximation method for the solution of Hammerstein–Volterra delay integral equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 105-110.
    3. Song, Huiming & Xiao, Yu & Chen, Minghao, 2021. "Collocation methods for third-kind Volterra integral equations with proportional delays," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    4. Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.
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