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Analysis of a new class of forward semi-Lagrangian schemes for the 1D Vlasov Poisson equations. (English) Zbl 1284.65145

Summary: The Vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles. It is self-consistently coupled with Poisson’s equation, which rules the evolution of the 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. An \(L^1\) convergence of the schemes is proved. Error estimates [in \({O\left(\Delta{t}^2+h^2 + \frac{h^2}{\Delta{t}}\right)}\) for Verlet] are obtained, where \(\Delta t\) and \(h = \max(\Delta x, \Delta v)\) are the discretization parameters.

MSC:

65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
35Q83 Vlasov equations
76X05 Ionized gas flow in electromagnetic fields; plasmic flow

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