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An hp-version Legendre collocation method for the third-kind VIEs with nonlinear vanishing delay

Author

Listed:
  • Guo, Yuling
  • Xu, Xiaoyu
  • Wang, Zicheng
  • Wang, Zhongqing

Abstract

This paper proposes an hp-version Legendre spectral collocation method for solving third-kind VIEs with nonlinear vanishing delay, which effectively addresses the singularity of the equation and the intricate impact of the delay term. The solvability of the algebraic system is established, and the convergence of the hp-version spectral collocation method under the L∞-norm is proved. Numerical experiments are performed to validate our theoretical predictions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:338-350
    DOI: 10.1016/j.matcom.2024.04.016
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    References listed on IDEAS

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    1. Sohrabi, S. & Ranjbar, H. & Saei, M., 2017. "Convergence analysis of the Jacobi-collocation method for nonlinear weakly singular Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 141-152.
    2. Yao, Guoqing & Tao, DongYa & Zhang, Chao, 2022. "A hybrid spectral method for the nonlinear Volterra integral equations with weakly singular kernel and vanishing delays," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    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. Chen, Hao & Ma, Junjie, 2022. "Solving the third-kind Volterra integral equation via the boundary value technique: Lagrange polynomial versus fractional interpolation," Applied Mathematics and Computation, Elsevier, vol. 414(C).
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