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Optimal superconvergence results for Volterra functional integral equations with proportional vanishing delays

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  • Ming, Wanyuan
  • Huang, Chengming
  • Zhao, Longbin

Abstract

In this paper, we develop a new technique to study the optimal convergence orders of collocation methods for Volterra functional integral equations with vanishing delays on quasi-geometric meshes. Basing on a perturbation analysis, we show that for m collocation points, the global convergence order of the collocation solution is only m. However, the collocation solution may exhibit superconvergence with order m+1 at the collocation points. In particular, the local convergence order may attain 2m−1 at the nodes, provided that the collocation is based on the m Radau II points. Finally, some numerical examples are performed to verify our theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:292-301
    DOI: 10.1016/j.amc.2017.09.045
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    References listed on IDEAS

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    1. 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. 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).
    2. 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.
    3. 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).

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