Numerical and analytical findings on the Volterra integral-algebraic index-1 system with vanishing delays

Shadi Malek Bagomghaleh, Saeed Pishbin and Gholamhossein Gholami

Applied Mathematics and Computation, 2024, vol. 466, issue C

Abstract: In the current study, we deal with a linear system of integral-algebraic-equations (IAEs) with vanishing delay arguments, which can be considered as the most momentous novelty of this work, since it is the first time where these two concepts have been combined. The so-called piecewise collocation scheme has been applied in order to numerically tackle the Hessenberg type IAEs system together with vanishing delays. Like always, this method confirms its solvability for these systems. Some well-established results in terms of regularity, existence, uniqueness, and also convergence of the solution for the problem under study have been presented masterly. Finally, two test problems have been fairly well-studied, for the sake of verifying theoretical achievements in practice.

Keywords: Integral-algebraic-equations (IAEs); Vanishing delays; Semi-explicit form; Piecewise collocation method; Uniqueness of the solution; Convergence analysis (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323006185

DOI: 10.1016/j.amc.2023.128449

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