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Convergence analysis of Jacobi spectral tau-collocation method in solving a system of weakly singular Volterra integral equations

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  • Mostafazadeh, Mahdi
  • Shahmorad, Sedaghat

Abstract

The main purpose of this paper is to solve a system of weakly singular Volterra integral equations using the Jacobi spectral tau-collocation method from two perspectives. Since the solutions of the main system exhibit discontinuity at the origin, classical Jacobi methods may yield less accuracy. Therefore, in the first approach, we transform the proposed system through a suitable transformation into an alternative type whose solutions are as smooth as desired. Subsequently, we derive a matrix formulation of the method and analyze its convergence properties in both L2 and L∞-norms.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:322-337
    DOI: 10.1016/j.matcom.2024.04.023
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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.
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