@article{Falah2024, 
author = {Hassanein Falah and Parviz Darania and Saeed Pishbin},
title = {Study of numerical treatment of functional first-kind Volterra integral equations},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {17414-17429},
keywords = {piecewise polynomial numerical method, delay integral equation, convergence analysis},
url = {https://www.sciopen.com/article/10.3934/math.2024846},
doi = {10.3934/math.2024846},
abstract = {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.}
}