Numerical method for the nonlinear Fokker-Planck equation

Journal Article · Tue Jul 01 04:00:00 EDT 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.56.1197· OSTI ID:526975

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

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1. Department of Chemistry and Department of Physics, University of Houston, Houston, Texas 77204-5641 (United States)
2. Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States)

A practical method based on distributed approximating functionals (DAFs) is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokker-Planck equation, and the method is compared with the accurate K-point Stirling interpolation formula finite-difference method. The approach is also used successfully to solve a nonlinear self-consistent dynamic mean-field problem for which both the cumulant expansion and scaling theory have been found by Drozdov and Morillo [Phys. Rev. E {bold 54}, 931 (1996)] to be inadequate to describe the occurrence of a long-lived transient bimodality. The standard interpretation of the transient bimodality in terms of the {open_quotes}flat{close_quotes} region in the kinetic potential fails for the present case. An alternative analysis based on the effective potential of the Schr{umlt o}dinger-like Fokker-Planck equation is suggested. Our analysis of the transient bimodality is strongly supported by two examples that are numerically much more challenging than other examples that have been previously reported for this problem. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 526975
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 1 Vol. 56; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
FEYNMAN PATH INTEGRAL
FOKKER-PLANCK EQUATION
FUNCTIONALS
INTERPOLATION
NONLINEAR PROBLEMS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
TIME DEPENDENCE