Numerical solution of a system of coupled non-linear integro-differential equations of Fredholm type

A method, based on a generalization of Runge-Kutta's method, is applied to a system of coupled integro-differenital equations of Fredholm type. It is shown that, under certain conditions, the related integral, containing an unknown variable, in each integro-differential equation can be approximated by a contraction operator, converging in the respective space concerned. Therefore they may be found by the method of iteration, starting from arbitrary values, and hence the given system may be solved, with a high degree of accuracy.