TY  - JOUR
AU  - Falah, Hassanein
AU  - Darania, Parviz
AU  - Pishbin, Saeed
PY  - 2024
TI  - Study of numerical treatment of functional first-kind Volterra integral equations
JO  - AIMS Mathematics
SP  - 17414
EP  - 17429
VL  - 9
IS  - 7
AB  - First-kind Volterra integral equations have ill-posed nature in comparison to the second-kind of these equations such that a measure of ill-posedness can be described by    ν-smoothing of the integral operator. A comprehensive study of the convergence and super-convergence properties of the piecewise polynomial collocation method for the second-kind Volterra integral equations (VIEs) with constant delay has been given in [1]. However, convergence analysis of the collocation method for first-kind delay VIEs appears to be a research problem. Here, we investigated the convergence of the collocation solution as a research problem for a first-kind VIE with constant delay. Three test problems have been fairly well-studied for the sake of verifying theoretical achievements in practice.
UR  - https://doi.org/10.3934/math.2024846
DO  - 10.3934/math.2024846