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Optimal Rate of Convergence of a Stochastic Particle Method to Solutions of 1D Viscous Scalar Conservation Law Equations

Mireille Bossy 1
1 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : The aim of this work is to present the analysis of the rate of convergence of a stochastic particle method for 1D viscous scalar conservation law equations. The convergence rate result is $\mathcal O(\D t + 1/\sqrt{N})$, where $N$ is the number of numerical particles and $\D t$ is the time step of the first order Euler scheme applied to the dynamic of the interacting particles.
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Submitted on : Wednesday, May 24, 2006 - 10:42:47 AM
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Mireille Bossy. Optimal Rate of Convergence of a Stochastic Particle Method to Solutions of 1D Viscous Scalar Conservation Law Equations. [Research Report] RR-3924, INRIA. 2000, pp.33. ⟨inria-00072728⟩

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