A Rosenau-type approach to the approximation of the linear Fokker--Planck equation
For researchers in numerical PDEs, this work offers an alternative perspective on approximating diffusion equations, but it is incremental as it adapts an existing technique.
The paper revisits the numerical approximation of the Fokker-Planck equation using a Rosenau-type approach, extending it to higher-order linear diffusion equations. The method provides consistent approximations, though no concrete numerical results are reported.
{The numerical approximation of the solution of the Fokker--Planck equation is a challenging problem that has been extensively investigated starting from the pioneering paper of Chang and Cooper in 1970. We revisit this problem at the light of the approximation of the solution to the heat equation proposed by Rosenau in 1992. Further, by means of the same idea, we address the problem of a consistent approximation to higher-order linear diffusion equations.