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

Mahdi Mostafazadeh and Sedaghat Shahmorad

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 223, issue C, 322-337

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.

Keywords: Jacobi polynomials; Tau-collocation method; Volterra integral equations; Smoothing transformation; Convergence analysis (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:223:y:2024:i:c:p:322-337

DOI: 10.1016/j.matcom.2024.04.023

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