Optimization of Calculations in Modeling the Breaking of Plasma Oscillations

The proposed method of optimization of calculations is of a combined nature. First, using a piecewise uniform grid, a McCormack-type difference scheme of the second order of accuracy is constructed, and, then, to weaken the stability condition, an implicit version of the scheme is used, which even in the nonlinear case allows for an iteration-free implementation. When constructing a grid, a preliminary study is required, which is based on the analytical properties of the solution to the differential problem. Based on the calculations carried out, it can be concluded that the potential reduction in the amount of calculations is dozens of times without a noticeable loss of accuracy.