A locally recursive non-locally asynchronous algorythm to RKDG methods for gas dynamics equations

In this paper we introduce the Runge-Kutta Discontinios Galerkin (RKDG) method for the Euler equations of the ideal gases in the one-dimentional case. Due to a piecewise-linear space approximation and a special Runge-Kutta time discretization, the second-order TVDM numerical scheme is obtained.
After analyzing the scheme dependency graph, we construct a locally recursive non-locally asynchronous algorythm (LRnLA) of its computation. The results of carried out tests are comparable with the numerical solutions by the other well-known methods of the same order.