An approximation method for solving systems of Volterra integro-differential equations

The approximate method for solving a system of nonlinear Volterra integro-differential equations introduced in this paper, involves the use of biorthogonal systems in adequate spaces of continuous functions associated with such a system. That allows to calculate, in an approximate way, the solution of such a system only by linear combinations of evaluations of adequate points at the basic functions and integrals of these functions, that are piecewise univariate and bivariate polynomials of degree one and two, respectively. We obtain an explicit control for the error, implement the method and illustrate the results with some numerical examples.