The Fokker-Planck Equation
نویسنده
چکیده
Stochastic differential equations (SDE) are used to model many situations including population dynamics, protein kinetics, turbulence, finance, and engineering [5, 6, 1]. Knowing the solution of the SDE in question leads to interesting analysis of the trajectories. Most SDE are unsolvable analytically and other methods must be used to analyze properties of the stochastic process. From the SDE, a partial differential equation can be derived to give information on the probability transition function of the stochastic process. Knowing the transition function gives information on the equilibrium distribution (if one exists), and convergence to the equilibrium distribution. The purpose of this paper and project is to study the numerical methods and applications as described in [9]. By Newton’s second law, the movement of a Brownian particle can be described by the differential equation, called the Langevin equation, given by
منابع مشابه
Pseudo-spectral Matrix and Normalized Grunwald Approximation for Numerical Solution of Time Fractional Fokker-Planck Equation
This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.
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