Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations. (arXiv:0912.4952v1 [math.NA])

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.

Published by

Original source : http://arxiv.org/abs/0912.4952...