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A hybrid spectral method for the nonlinear Volterra integral equations with weakly singular kernel and vanishing delays

Author

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  • Yao, Guoqing
  • Tao, DongYa
  • Zhang, Chao

Abstract

In this paper, we develop a hybrid spectral method for the nonlinear second-kind Volterra integral equations (VIEs) with weakly singular kernel and vanishing delays. Our main strategy is to divide the original interval into subintervals, to employ the shifted generalized log orthogonal functions (GLOFs) as the basis on the first interval, to take the classical shifted Legendre polynomials as the basis on other intervals. We analyze the existence and uniqueness of the numerical scheme, and derive the corresponding error estimates. A series of examples demonstrate the effectiveness of the proposed method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:417:y:2022:i:c:s0096300321008626
    DOI: 10.1016/j.amc.2021.126780
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    Cited by:

    1. Lu, Jiashu & Yang, Mengna & Nie, Yufeng, 2022. "Convergence analysis of Jacobi spectral collocation methods for weakly singular nonlocal diffusion equations with volume constraints," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    2. 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.
    3. Ahmed Z. Amin & Mahmoud A. Zaky & Ahmed S. Hendy & Ishak Hashim & Ahmed Aldraiweesh, 2022. "High-Order Multivariate Spectral Algorithms for High-Dimensional Nonlinear Weakly Singular Integral Equations with Delay," Mathematics, MDPI, vol. 10(17), pages 1-20, August.

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