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Super-convergence analysis of collocation methods for linear and nonlinear third-kind Volterra integral equations with non-compact operators

Author

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  • Song, Huiming
  • Yang, Zhanwen
  • Xiao, Yu

Abstract

This paper concerns iterated collocation methods for linear and nonlinear Volterra integral equations (VIEs) of the third kind with noncompact operators. The optimal global and local super-convergence orders are determined under a new mesh. Finally, some numerical examples are provided to verify the convergence results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006469
    DOI: 10.1016/j.amc.2021.126562
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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. 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).
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