On numerical Landau damping for splitting methods applied to the Vlasov-HMF model
Numerical Analysis
2015-10-23 v1
Abstract
We consider time discretizations of the Vlasov-HMF (Hamiltonian Mean-Field) equation based on splitting methods between the linear and non-linear parts. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that the numerical solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping. Moreover, we prove that the modified state is close to the continuous one and provide error estimates with respect to the time stepsize.
Keywords
Cite
@article{arxiv.1510.06555,
title = {On numerical Landau damping for splitting methods applied to the Vlasov-HMF model},
author = {Erwan Faou and Romain Horsin and Frédéric Rousset},
journal= {arXiv preprint arXiv:1510.06555},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1403.1668