Numerical approaches for systems of Volterra-Fredholm integral equations

In this work we introduce two numerical methods for solving systems of Volterra--Fredholm integral equations. In the nonlinear case we suggest a fixed point method, where the iterations are perturbed in a suitable way according to a Schauder basis in the Banach space of continuous functions C[a,b]². In the linear case we propose a collocation method based on a particular class of approximating functions. In both methods, convergence analysis and/or low computational cost are analysed, taking into account the properties of the basis under consideration. Numerical results confirm the theoretical study.