Biorthogonal systems for solving Volterra integral equation systems of the second kind (Q629424)

The authors generalizes the iterative method to solve the system of Volterra integral equations of the second kind \[ X(t)=Y_{0}(t)+\int_{0}^{t}K(x,s,X(s))ds,\qquad t\in[\alpha,\alpha+\beta], \] where \(X(t)\in\mathbb R^{n}\). The Lipschitz condition assumed for \(K\) and a fixed point theorem allow to establish the existence of a unique solution. The approximate solution by this method is obtained in analytical form, only the absolute error is evaluated numerically.