Abstract
In this paper, we study a class of block collocation boundary value methods for the first-kind Volterra integral equations. The numerical algorithm is constructed by utilizing approximations to the exact solution in future steps. The solvability of the new method is not ensured, even for the uniform mesh. Therefore, we discuss its solvability by studying the special structure of the collocation equation and present the sufficient condition for the existence of the collocation solution. Furthermore, we exploit the convergence property with the help of interpolation remainders. Finally, numerical experiments are conducted to show the effectiveness of the new boundary value method and verify given theoretical results.
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