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We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

In this paper, we propose a method to approximate the fixed point of an operator in a Banach space.Using biorthogonal systems, this method is applied to build an approximation of the solution of a class of nonlinear partial integro-differential equations. The theoretical findings are illustrated with several numerical examples, confirming the reliability, validity and precision of the proposed method.