J M Donoso et al 1999 J. Phys. A: Math. Gen. 32 3681 doi:10.1088/0305-4470/32/20/302
Short-time propagators for nonlinear Fokker-Planck equations
J M Donoso, J J Salgado and M Soler
Show affiliationsPath-integral solutions to time-evolution equations in statistical physics have recently aroused great interest. The main problem in applying these methods is to find a valid propagator in the short-time regime of evolution. A new method is proposed to obtain a set of accurate short-time propagators by the construction of a simple auxiliary Fokker-Planck equation. This equation takes into account the full relevant functional dependence of the original drift and diffusion terms. By using a suitable decomposition of the drift and diffusion coefficients it is possible to derive a new representation of the Dirac 
-function. From this representation the short-time behaviour of the solutions is given not only for the infinitesimal time interval, but also for a discrete finite one which has a more practical numerical sense. This picture leads to accurate short-time propagators which include the prescribed boundary conditions.
- PACS
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05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)
- MSC
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82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
- Subjects
- Dates
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Issue 20 (21 May 1999)
Received 14 August 1998, in final form 23 February 1999
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Short-time propagators for nonlinear Fokker-Planck equations
J M Donoso et al 1999 J. Phys. A: Math. Gen. 32 3681
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