求解分数阶对流弥散方程的边界值法  

BOUNDARY VALUE METHODS FOR SOLVING THE FRACTIONAL ADVECTION DISPERSION EQUATION

作　　者：杨淑伶[1] 

机构地区：[1]广东工业大学应用数学学院,广州510006

出　　处：《高等学校计算数学学报》2016年第4期350-356,共7页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金面上项目(31670391);广东省科技计划项目(2013B051000075)

摘　　要：在现代地下水动力学研究中，对流弥散方程常用来刻画污染物等的运移过程．但在介质不纯或不规则的分形多孔介质情况下，穿透曲线的实测数据呈不对称的偏态分布，即存在提前穿透和拖尾的现象.研究表明，此时污染物的运移过程已从局域性的布朗运动改变为非局域性的Levy过程，考虑到分数阶导数与反常扩散过程在本质上相类似，因而分数阶对流弥散方程（FADE）被引入以取代传统的整数阶对流弥散方程．A one-dimensional spatial fractional avdvection dispersion equation is considered in this paper. The finite difference scheme with the shifted Griinwald formula is firstly applied to discrete the spatial derivative of the equation. Then the temporal discretization by the boundary value methods can transfer the equa- tion to a large linear system. The GMRES iterative method is employed to solving the resulting linear system and a preconditioner is constructed to accelerate the convergence. Numerical examples demonstrate the superiority of this algorithm.

关 键 词：对流弥散方程 分数阶导数 边界值 分形多孔介质 求解 地下水动力学 LEVY过程 运移过程 

分 类 号：O241.6[理学—计算数学] O241.8[理学—数学]