Adaptive Gaussian particle method for the solution of the Fokker-Planck equation

2012

The Fokker-Planck equation describes the evolution of the probability density for a stochastic ordinary differential equation (SODE). A solution strategy for this partial differential equation (PDE) up to a relatively large number of dimensions is based on particle methods using Gaussians as basis functions. An initial probability density is decomposed into a sum of multivariate normal distributions and these are propagated according to the SODE. The decomposition as well as the propagation is subject to possibly large numeric errors due to the difficulty to control the spatial residual over the whole domain. In this paper a new particle method is derived, which allows a deterministic error…