An Efficient Time-splitting Fourier Spectral Method For The Vlasov-Poisson System

Vlasov-Poisson equations is widely applied in the research of plasma physics equa-tion,and is a kind of important Mechanical model of astrophysics and plasma physics. It can describe the movement of nebula and the evolution of plasma physics. Vlasov Poisson equations is a kind of nonlinear partial differential equations, so far, people haven’t found its analytical solution. Therefore, only finding the numerical solution of it can research the plasma physics phenomenon. This paper will design a highly efficient Numerical calculation method to the Vlasov-Poisson equations,which is time-splitting-Fourier spectral method.Specifically,we use time-splitting scheme in time direction, and use Fourier spectral method in the space variable direction and speed variable direction. This paper respectively gives the one and two dimension of Vlasov-Poisson equations Algorithm in detail, and examples of calculation, gets the results of numerical calcula-tion, again according to the results of numerical studies related physical phenomena.We also give the four conserved quantities of one and two dimension of Vlasov-Poisson equations demonstrate in detail respectively, to justify the stability and reliability of the time-splitting-Fourier spectral method. Finally, the results of numerical calculation method are adopted in this paper also verify the four conserved quantity.