Convergence of a Random Walk Method for the Burgers Equation
نویسندگان
چکیده
We show that the solution of the Burgers equation can be approximated in LX(R), to within 0(m~1/*(lnm)2), by a random walk method generated by 0(m) particles. The nonlinear advection term of the equation is approximated by advecting the particles in a velocity field induced by the particles. The diffusive term is approximated by adding an appropriate random perturbation to the particle positions. It is also shown that the corresponding viscous splitting algorithm approximates the solution of the Burgers equation in LX(R) to within 0(k) when k is the size of the time step. This work provides the first proof of convergence in a strong sense, for a random walk method, in which the related advection equation allows for the formation of shocks.
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