Convergence of a Difference Scheme for the Vlasov--Poisson--Fokker--Planck System in One Dimension
Convergence of a Difference Scheme for the Vlasov--Poisson--Fokker--Planck System in One Dimension
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DOI：
10.1137/s0036142996302554
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发表时间：
1998-06
影响因子：
2.9
通讯作者：
Jack Schaeffer
中科院分区：
文献类型：
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作者：
Jack Schaeffer
对周期一维Vlasov-Poisson-Fokker-Planck系统提出了一种有限差分格式，该格式与[C.\cheng和G.\knorr，22(1976)，pp.330--351]中的格式有关。密度f Left(t，x，v right)和电场E Left(t，x right)分别收敛到L^{2}$和L^{inty}$中的精确解值.收敛速度本质上是一阶的。该方案已在[J.\Schaeffer，中心非线性分析研究报告97-NA-004，Carnegie Mellon University，1997]中实现，并与随机粒子方法进行了比较。
A finite difference scheme is proposed for the periodic one-dimensional Vlasov--Poisson--Fokker--Planck system which is related to the scheme in [C.\ Cheng and G.\ Knorr, {\em J. Comp.\ Phys}., 22 (1976), pp. 330--351]. The density $f \left( t,x,v \right) $ and the electric field $E \left(t,x \right) $ are shown to converge to the exact solution values in $L^{2}$ and $L^{\infty }$, respectively. The rate of convergence is essentially first order. This scheme has been implemented in [J.\ Schaeffer, Center for Nonlinear Analysis Research Report 97-NA-004, Carnegie Mellon University, 1997] and compares favorably with a random particle method.