数值求解Lévy-Feller扩散方程

Abstract

<正>1 引言在物理化学领域经常会出现微粒的不规则扩散现象,许多学者试图用某种数学模型来解释此现象．Gorenflo等[1]提出了一种有效的数学模型,即用阶数为α∈(0,2]且含有偏斜度θ(|θ|≤min{α,2-α})的Riesz-Feller位势Dθα代替标准扩散方程中的二阶空间导数．算子Dθα描述的扩散现象就称作Levy-Feller扩散,而含此算子的的方程就称为

In this paper, we consider the space fractional Levy-Feller diffusion equation with Riesz-Feller potential. By using the equivalent of fractional order differential operators, an new finite difference method for discreting the above diffusion equation is proposed. The stability and convergence of the method are analysed. Finally, a numerical example is provided to show that the finite difference method for solving FPDE is an effective method.