DISTRIBUTED APPROXIMATING FUNCTIONAL-APPROACH TO THE FOKKER-PLANCK EQUATION - TIME PROPAGATION

The Fokker-Planck equation is solved by the method of distributed appr oximating functionals via forward time propagation. Numerical schemes involving higher-order terms in Delta t are discussed for the time dis cretization. Three typical examples (a Wiener process, an Orntein-Uhle nbeck process, and a bistable diffusion model) are used to test the ac curacy and reliability of the present approach, which provides solutio ns that are accurate up to ten significant figures while using a small number of grid points and a reasonably large time increment. Two sets of solutions for the bistable system, one computed using the eigenfun ction expansion of a preceding paper and the other using the present t ime-dependent treatment, agree to no fewer than five significant figur es. It is found that the distributed approximating functional method, while simple in its implementation, yields the most accurate numerical solutions yet available for the Fokker-Planck equation. (C) 1997 Amer ican Institute of Physics.