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In this paper, we present a collocation method for nonlinear Volterraintegral equation of the first kind. This method benefits from the idea of$hp$-version projection methods. We provide an approximation based on theLegendre polynomial interpolation. The convergence of the proposed method iscompletely studied and an error estimate under the $L^2$-norm is provided.Finally, several numerical experiments are presented in order to verify theobtained theoretical results.

$ hp $-version collocation method for a class of nonlinear Volterra integral equations of the first kind