Numerical evaluation of path-integral solutions to Fokker-Planck equations. III. Time and functionally dependent coefficients

Journal Article · Sun Feb 15 04:00:00 EST 1987 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.35.1795· OSTI ID:7015173

Wehner, M F; Wolfer, W G

A path-integral solution to truly nonlinear Fokker-Planck equations is derived. Such equations exhibit in the drift and diffusion coefficients a functional dependence on the distribution function. This type of implicit time dependence is shown to introduce terms into the propagator function of the exact same order in the time step tau, as does an explicit time dependence if the functional dependence is sufficiently smooth. A standard discrete lattice formulation of the path integral is then used to reproduce the appropriate, truly nonlinear Fokker-Planck equation. This discrete formulation provides a basis for an efficient numerical algorithm and is applied with excellent results to several example problems where exact solutions can be calculated.

• Research Organization: Lawrence Livermore National Laboratory, University of California, P.O. Box 5508, Livermore, California 94550
• OSTI ID: 7015173
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 35:4; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHEMICAL REACTION KINETICS
DIFFERENTIAL EQUATIONS
EQUATIONS
FEYNMAN PATH INTEGRAL
FOKKER-PLANCK EQUATION
INTEGRALS
KINETICS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
REACTION KINETICS
TIME DEPENDENCE