Based On Adomian Decomposition Method Of The Study Of Fokker - Planck Equation Solution

Fokker-Planck equation (referred to as the FP equation)have an important position in many natural sciences, such as astrophysics, quantum optics, nuclear, so many scientists are trying to study the problem of the efficient solution of this equation. Adomian decomposition method is solving the approximate solution of linear and nonlinear equations. Through a number of theoretical reasoning of scientists, the Adomian decomposition method is proved faster than any other method of solving equations,which can obtain the higher accuracy of the approximate solution and can be used to approximate the true solution to any required precision. In this paper, Adomian decomposition method, the FP equations, the FP equation is determined by the drift coefficient A(x) and the diffusion coefficient B(x) equation.We use the Adomian decomposition method to study coefficient of a given FP equation. the research contents and the results as follows:(1) Predecessors in the solution of one-dimensional linear and time-independent FP equation,A(x) and B(x) in the equation of the given real number, the work of the previous in-depth study,A(x)、B(x) extended for any real number FP equation. Prove that the use of Adomian decomposition method to get the approximate solution of the equation analytical solution. Adomian decomposition method for solution of one-dimensional linear time-relate A(x,t)=e’cot(x)cos(x)+e’sin(x)-cot(x) and B(x,t)=e’cos(x) of the FP equation,get the approximate solution is also analytic solution.(2) The same PF equation, Adomian decomposition method for solution of Two-dimensional linear and time-independent and the drift coefficient A1(x1,x2)=a1x1, A2(x1,x2)-b1x3and the diffusion coefficient B1,1(x1,x2)=a2x22,B1,2(x1,x2)=x1, B2,1(x1,x2)=b2x22,B2,2(x1,x2)=b2x22, as determined by the approximate solution of the equation the analytical solution. But In the two-dimensional linear time-related and the drift coefficient A1(x1,x2,t)=(x1+x2)t,A2(x1,x2,t)=x1t and the diffusion coefficient B1,1(x1,x2,t)=a,B1,2(x1,x2,t)=x1,B2,1(x1,x2,t)=b,B2,2(x1,x2,t)=x2of the PF equation, Adomian decomposition method can not be the concrete expression of the approximate solution of the equation, the available approximate solution of the concrete form of the decomposition rate, decomposition rate and the exact solution the error between the value can be different according to the selected independent variables and different error values given in this paper range from10-15to0.1.(3) For FP equation, one dimensional and two dimensional nonlinear coefficient are given FP equation, the approximate solution and the analytical solution are same for using the Adomian decomposition method.