一维Vlasov-Poisson方程的一类新型前向半拉格朗日格式分析
Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations
AI总结：
针对Vlasov-Poisson系统，提出基于Cauchy-Kovalevsky过程的新型前向半拉格朗日格式，证明其守恒性和L1范数收敛性并给出误差估计。
摘要：
Vlasov方程是描述带电粒子演化的动力学模型，与泊松方程耦合，后者控制自洽电场的演化。本文针对Vlasov-Poisson系统，基于Cauchy-Kovalevsky (CK)过程数值求解特征曲线，引入了一类新型前向半拉格朗日格式。推导了格式对分布函数前几阶矩的精确守恒性质，并进行了收敛性研究，该研究同时适用于CK格式和更经典的Verlet格式。证明了格式在L1范数下的收敛性，并得到了误差估计。
英文摘要：
The Vlasov equation is a kinetic model describing the evolution of charged particles, and is coupled with Poisson's equation, which rules the evolution of the self-consistent electric field. In this paper, we introduce a new class of forward Semi-Lagrangian schemes for the Vlasov-Poisson system based on a Cauchy Kovalevsky (CK) procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. The convergence in L1 norm of the schemes is proved and error estimates are obtained.
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