A Deterministic Approximation of Diffusion Equations Using Particles

A new particle method adapted to the simulation of convection-diffusion problems is presented. The method relies on the definition of a convective field associated with the heat operator, which allows the convection of the particles in a deterministic way.No rigorous error analysis is given but, instead, a detailed numerical study of the influence of the parameters is presented. This study is performed on the heat equation, then applied to a Fokker–Planck model arising in the kinetic theory of plasma physics. Finally, an extension of the method to other problems is given.