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In this paper we focus on WENO-based methods for the simulation of the 1DQuasi-Relativistic Vlasov--Maxwell (QRVM) model used to describe how a laserwave interacts with and heats a plasma by penetrating into it. We proposeseveral non-oscillatory methods based on either Runge--Kutta (explicit) orTime-Splitting (implicit) time discretizations. We then show preliminarynumerical experiments.

WENO schemes applied to the quasi-relativistic Vlasov--Maxwell model for laser-plasma interaction