In this work, an exponential Discontinuous Galerkin (DG) method is proposed to solve numerically Vlasov type equations. The DG method is used for space discretization which is combined exponential Lawson Runge-Kutta method for time discretization to get high order accuracy in time and space. In addition to get high order accuracy in time, the use of Lawson methods enables to overcome the stringent condition on the time step induced by the linear part of the system. Moreover, it can be proved that a discrete Poisson equation is preserved. Numerical results on Vlasov-Poisson and Vlasov Maxwell equations are presented to illustrate the good behavior of the exponential DG method.

翻译：本文提出一种指数间断伽辽金（DG）方法，用于数值求解弗拉索夫型方程。该方法采用DG进行空间离散，并结合指数型Lawson龙格-库塔方法进行时间离散，从而在时间与空间维度上获得高阶精度。除实现时间高阶精度外，Lawson方法的使用还有助于克服由系统线性部分引起的时间步长严格限制条件。此外，可证明离散泊松方程得以保持。文中通过弗拉索夫-泊松方程与弗拉索夫-麦克斯韦方程的数值算例，展示了指数DG方法的良好性能。