Convergence Rate for the Approximation of the Limit Law of Weakly Interacting Particles: Application to the Burgers Equation
نویسنده
چکیده
In this paper we construct a stochastic particle method for the Burgers equation with a monotone initial condition; we prove that the convergence rate is O(1= p N + p t) for the L 1 (IR)-norm of the error. To obtain that result, we link the PDE and the algorithm to a system of weakly interacting stochastic particles; the diiculty of the analysis comes from the discontinuity of the interaction kernel which is equal to the Heaviside function. In 4], we show how the algorithm and the result extend to the case of non monotone initial conditions for the Burgers equation. We also treat the case of nonlinear PDE's related to particle systems with Lipschitz interaction kernels. Our next objective is to adapt our methodology to the (more diicult) case of the 2-D inviscid Navier-Stokes equation.
منابع مشابه
Convergence Rate for the Approximation of the Limit Law of Weakly Interacting Particles 1: Smooth Interacting Kernels
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تاریخ انتشار 1996