High precision simulation algorithms are proposed and justified for modelling cold plasma oscillations taking into account electron–ion collisions in the non-relativistic case. The specific feature of the approach is the use of Lagrangian variables for approximate solution of the problem formulated initially in Eulerian variables. High accuracy is achieved both through the use of analytical solutions on trajectories of particles and due to sufficient smoothness of the solution in numerical integration of Cauchy problems. Numerical experiments clearly illustrate the obtained theoretical results. As a practical application, a simulation of the well-known breaking effect of multi-period relativistic oscillations is carried out. It is shown that with an increase in the collision coefficient one can observe that the breaking process slows down until it is completely eliminated.

中文翻译：

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考虑电子-离子碰撞的用于求解冷等离子体方程系统的高精度方法

考虑到非相对论情况下的电子 - 离子碰撞，提出并证明了高精度模拟算法用于模拟冷等离子体振荡。该方法的具体特点是使用拉格朗日变量来近似求解最初用欧拉变量制定的问题。通过对粒子轨迹使用解析解以及在柯西问题的数值积分中解的足够平滑，可以实现高精度。数值实验清楚地说明了所获得的理论结果。作为实际应用，对众所周知的多周期相对论振荡的破坏效应进行了模拟。