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Foundations of Computational Mathematics

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14-10-2016

On Numerical Landau Damping for Splitting Methods Applied to the Vlasov–HMF Model

Authors: Erwan Faou, Romain Horsin, Frédéric Rousset

Published in: Foundations of Computational Mathematics | Issue 1/2018

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Abstract

We consider time discretizations of the Vlasov–HMF (Hamiltonian mean-field) equation based on splitting methods between the linear and nonlinear 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 step size.

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Title: On Numerical Landau Damping for Splitting Methods Applied to the Vlasov–HMF Model
Authors: Erwan Faou
Romain Horsin
Frédéric Rousset
Publication date: 14-10-2016
Publisher: Springer US
Published in: Foundations of Computational Mathematics / Issue 1/2018
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI: https://doi.org/10.1007/s10208-016-9333-9

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