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 the following second order integro-differential boundary value problem ν(y)g(y)=∫0∞k(x)g(x)dx(D(y)g′(y))′+p(y),g′(0)=0,limy→+∞g(y)=0, 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.