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))′(y), g′(0) = 0,lim y→+∞ 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. © 2012 Elsevier Ltd. All rights reserved.
Basile, M., Messina, E., Themistoclakis, W., & Vecchio, A. (2012). A numerical method for a class of non-linear integro-differential equations on the half line. In Computers and Mathematics with Applications (Vol. 64, pp. 2354–2363). https://doi.org/10.1016/j.camwa.2012.06.007