A numerical method for a class of non-linear integro-differential equations on the half line

We design and analyse a numerical method for the solution of a particular second order integro-differential boundary value problem on the semiaxis, which arises in the study of the kinetic theory of dusty plasmas. The method we propose represents a first insight into the numerical solution of more complicated problems and consists of a discretization of the differential and integral terms and of an iteration process to solve the resulting non-linear system. Under suitable hypotheses we prove the convergence. We will show the characteristics of the method by means of some numerical simulations.