Distributed approximating functional approach to the Fokker{endash}Planck equation: Time propagation

Journal Article · Fri Aug 01 04:00:00 EDT 1997 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.474674· OSTI ID:589432

Wei, G W; Zhang, D S; Kouri, D J ^[1]; Hoffman, D K ^[2]

---

1. Department of Chemistry and Department of Physics, University of Houston, Houston, Texas 77204-5641 (United States)
2. Department of Chemistry and Ames Laboratory (United States)

The Fokker{endash}Planck equation is solved by the method of distributed approximating functionals via forward time propagation. Numerical schemes involving higher-order terms in {Delta}t are discussed for the time discretization. Three typical examples (a Wiener process, an Ornstein{endash}Uhlenbeck process, and a bistable diffusion model) are used to test the accuracy and reliability of the present approach, which provides solutions 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 eigenfunction expansion of a preceding paper and the other using the present time-dependent treatment, agree to no fewer than five significant figures. 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{endash}Planck equation. {copyright} {ital 1997 American Institute of Physics.}

• Research Organization: Ames National Laboratory
• DOE Contract Number: W-7405-ENG-82
• OSTI ID: 589432
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 8 Vol. 107; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
CHEMICAL REACTIONS
DIFFUSION
FOKKER-PLANCK EQUATION
NUMERICAL SOLUTION
STATISTICAL MECHANICS
STOCHASTIC PROCESSES