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Convergence analysis of the Jacobi-collocation method for nonlinear weakly singular Volterra integral equations

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  • Sohrabi, S.
  • Ranjbar, H.
  • Saei, M.

Abstract

In this work, we present an efficient spectral-collocation method for numerical solution of a class of nonlinear weakly singular Volterra integral equations. This type of equations typically has a singular behavior at the left endpoint of the interval of integration. For overcoming this non-smooth behavior, we apply the Jacobi-collocation method. The convergence analysis of the proposed method is investigated in the L∞ and the weighted L2 norms and the results of several numerical experiments are presented which support the theoretical results. The computed results are compared wherever possible with those already available in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:299:y:2017:i:c:p:141-152
    DOI: 10.1016/j.amc.2016.11.022
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    References listed on IDEAS

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    1. Ma, Xiaohua & Huang, Chengming & Niu, Xin, 2015. "Convergence analysis of spectral collocation methods for a class of weakly singular Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 131-144.
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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. Mostafazadeh, Mahdi & Shahmorad, Sedaghat, 2024. "Convergence analysis of Jacobi spectral tau-collocation method in solving a system of weakly singular Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 322-337.
    3. Yu, Hao & Wu, Boying & Zhang, Dazhi, 2018. "A generalized Laguerre spectral Petrov–Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 96-111.
    4. 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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