A deterministic particle method for transport diffusion equations: Application to the Fokker-Planck equation
This paper considers various classes of diffusion equations and introduces a particle method for their solution. The Fokker-Planck equation is examined in detail which describes fast ion transport in a background plasma. The simplest equation considered however is \(\partial f/\partial t-\sigma (\partial^ 2f)/\partial x^ 2=0\) with \(f(x,0)=f_ 0\). The particle approximation consists of replacing \(f_ 0\) by a linear combination of Dirac functions. The time dependence is approximated by a simple explicit Euler scheme and a stability condition is given.
scientific article; zbMATH DE number 4102445