On second-order accuracy schemes for modeling of plasma oscillations

For modeling cold plasma oscillations in the non-relativistic and relativistic cases, some modifications of classical difference schemes of the second order of accuracy are proposed: the McCormack method and the two-stage Lax-Wendroff method. Previously, only the first-order accuracy scheme was known for calculations in Euler variables. For the problem of free plasma oscillations initiated by a short high-power laser pulse, the results of numerical experiments on energy conservation and other quantities were performed in order to test the proposed schemes. It is concluded that the numerical analysis of oscillations is reliable both for the McCormack scheme and for the Lax-Wendroff scheme; however, for the calculation of "long-lived" processes, the first scheme is more preferable. The theoretical analysis of approximation and stability together with experimental observations of quantitative characteristics of errors for the most sensitive quantities significantly increases the reliability of calculations.