Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 Articles in Press 2026 07 17 Spline collocation method for solving the third-kind Volterra integral equations 1 6 10806 10.22075/ijnaa.2024.35545.5287 EN Ali Davari Department of Mathematics, Khansar Campus, University of Isfahan, Iran. Journal Article 2023 10 06 In this paper, we consider the Volterra integral equations (VIEs) of the third kind. A procedure, using spline functions, for obtaining<br />approximate solutions to Volterra integral equations of the third kind is presented. We develop an efficient spline collocation method for solving this type of equations. The proposed scheme is especially suited for VIEs in polynomial spline space, due to its essential feature of local approximations on subintervals. We then use these results in the convergence analysis of a polynomial spline collocation method for solving such problems numerically. The solvability of spline collocation methods is accessed, and the convergence analysis is studied. Numerical results confirm the spectral accuracy and the theoretical results of the proposed method. The third-kind Volterra functional integral equations Spline collocation method Convergence analysis https://ijnaa.semnan.ac.ir/article_10806_9113c52c5f26af1782e6bf7c56973ef4.pdf