QUICK Discrete Schemes For Fokker-Planck Equations

Fractional differential equations have rich theoretical connotations and far-reaching physical meanings.They can more accurately and concisely describe the complex mechanics and physical processes with historical memory in some practical problems.In this paper,we considers the following time fractional Fokker-Planck equation(?)(0.3)It's two-dimensional form is(?)(0.4)where ? ?(0,1),k? is the generalized diffusion coefficient,f,g is the varying external force field,G is the source term and(?)?w/(?)t? is the ? order Caputo fractional derivative.To numerically solve the Fokker-Planck equation with external force field,we study a finite volume method that uses QUICK scheme to discretize the convection term,where the external force field is a function in space varialble x.In our method,the diffusion term is discretized by using the central difference scheme,the convection term is discretized by the QUICK scheme,and the time fractional order derivative is approximated by the L1 scheme.Finally,numerical experiments show that the method is second-order in space and 2-? order in time.This paper is divided into five chapters as follows:In Chapter 1,we introduce the research background and current situation of the thesis and expound the research work and innovation points.In Chapter 2,we introduce some related concepts and basic properties of fractional derivatives.In Chapter 3,we design a full-discrete method for one-dimensional fractional Fokker-Planck equation.In Chapter 4,we design a full-discrete method for two-dimensional fractional Fokker-Planck equation.In Chapter 5,we we verify the availability of our method through some numerical examples.