Numerical solution of two-dimensional Fokker-Planck equations. (English) Zbl 1083.82526
Summary: We present a robust finite difference scheme for the integration of the Fokker-Planck (FP) equation with two variables plus time. The scheme is checked with problems where analytic solutions exist and it is compared with finite element codes, as well as with simulations of the associated Stochastic Differential Equation (SDE). The precision and stability of the scheme are verified.
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 82-08 | Computational methods (statistical mechanics) (MSC2010) |
| 65C99 | Probabilistic methods, stochastic differential equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
Keywords:
Nonlinear beam dynamics; Stochastic processes; Fokker-Planck equation; Finite difference scheme; Operator splitting methodReferences:
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