On perturbative approach to the one-dimensional Fokker-Planck equation
| Autor: | Yan-Min Dai, 戴彥民 |
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| Rok vydání: | 2007 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 95 The purpose of this thesis is to present a direct perturbative method to solving certain Fokker-Planck equation, which have constant diffusion coefficients and some small parameters in the drift coefficients. In the second chapter, we describe how Einstein explained Brownian movement by stochastic method. After Einstein, Fokker and Planck distributed this diffusion equation with the condition of extra force field. In this chapter, we have an example to illustrate how the extra force field influences the diffusion of Brown particles. In chapter three, we solve the Fokker- Plank equation by the method of eigen- value expansion. We have two examples to describe the practicability of this method. It is not always easy to solve Fokker-Planck equations with time-independent diffusion and drift coefficients. Needless to say, finding exact solution of the Fokker- Planck equation with time-dependent drift coefficients is also very difficult in general. In final chapter, we will discuss a perturbation method to solve the one-dimension Fokker-Planck equation with a constant diffusion coefficient and time-dependent drift coefficient. Two examples are used to show that such perturbative method can be a useful way to obtain the approximate solutions of the Fokker-Planck equation. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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