Analytical and numerical solutions of one-dimensional cold plasma equations

High-accuracy numerical algorithms are proposed and justified for the simulation of cold plasma oscillations in both nonrelativistic and relativistic cases. A specific feature of the given approach is that Lagrangian variables are used for the approximate solution of the problem formulated in Eulerian variables. The main results are stated as convergence theorems for the proposed algorithms with respect to small discretization parameters of independent Eulerian variables. The theoretical results are illustrated by numerical experiments. Specifically, the breaking of plasma oscillations is modeled and this effect is confirmed to have the form of a gradient catastrophe.