In this paper a multistep collocation method for solving Volterra integral equations of the third kind is explained and analyzed. The structure of the method, its solvability and convergence analysis are investigated. Moreover to show the applicability of the presented method and to confirm our theoretical results some numerical examples are given. Keywords Volterra integral equations of the third kind • Collocation method • Multistep collocation method Mathematics Subject Classification 45A05 • 45D05 • 45E99 where 0 ≤ α < 1, 0 < β ≤ 1, f (x) = x β g(x) with g(x) ∈ C(I), k is a real continuous function defined on D = {(x, t) : 0 ≤ t ≤ x ≤ T } and y(x) is an unknown function. Volterra integral equations of the third kind have appeared in modeling numerous problems in various branches of science and engineering, such as heat transfer, population growth models Communicated by Hui Liang.
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