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

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.

Automated summary

This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.