Rusanov’s third-order accurate scheme for modeling plasma oscillations

A modification of the well-known Rusanov third-order accurate scheme is proposed for modeling nonrelativistic oscillations of a cold plasma. Only first- and second-order accurate schemes were used earlier for similar computations in Eulerian variables. In the case of a test problem with a smooth solution, the errors of the constructed scheme are investigated and compared with the errors of the MacCormack scheme. For the problem of free plasma oscillations induced by a short intense laser pulse, numerical results are presented concerning the conservation of energy and an additional function for both schemes and the accuracy of the electron density in the center of the domain. It is concluded that the Rusanov scheme is superior theoretically, although the MacCormack scheme is more suitable for applications, primarily, for computations of long-lived processes and cold plasma oscillations similar to actual ones. A theoretical analysis of approximation and stability, together with experimental observations of quantitative characteristics of the error for the most sensitive quantities, significantly improves the reliability of the computations.