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Collocation methods for third-kind Volterra integral equations with proportional delays

Author

Listed:
  • Song, Huiming
  • Xiao, Yu
  • Chen, Minghao

Abstract

In this paper, a class of Volterra delay integral equations (VDIEs) with noncompact operators is approximated by collocation methods. The properties of corresponding operators as well as existence, uniqueness and regularity of exact solution are discussed. The existence and uniqueness of collocation solutions are proved under two special graded meshes. Moreover, we present the convergence conditions and convergence order. Finally, some numerical examples are given to verify the validity of the theoretical orders of convergence.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:388:y:2021:i:c:s0096300320304677
    DOI: 10.1016/j.amc.2020.125509
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    References listed on IDEAS

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    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. Ming, Wanyuan & Huang, Chengming, 2017. "Collocation methods for Volterra functional integral equations with non-vanishing delays," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 198-214.
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    Cited by:

    1. 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.
    2. Song, Huiming & Yang, Zhanwen & Xiao, Yu, 2022. "Super-convergence analysis of collocation methods for linear and nonlinear third-kind Volterra integral equations with non-compact operators," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    3. Guo, Yuling & Xu, Xiaoyu & Wang, Zicheng & Wang, Zhongqing, 2024. "An hp-version Legendre collocation method for the third-kind VIEs with nonlinear vanishing delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 338-350.

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    2. 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.
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