一类反常次扩散方程Neumann问题的有限差分格式及收敛性分析  

A Finite Difference Scheme and a Convergence Analysis of a Kind of Anomalous Diffusion Equation with Neumann Conditions

作　　者：马亮亮[1] 刘冬兵[1] 

机构地区：[1]攀枝花学院数学与计算机学院,四川攀枝花617000

出　　处：《五邑大学学报（自然科学版）》2014年第1期1-4,9,共5页Journal of Wuyi University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(No.60673192);四川省科技厅资助项目(2013JY0125)

摘　　要：利用一阶向前差商和空间二阶中心差商以及高阶线性多步法公式构造了反常次扩散方程Neumann问题的有限差分格式,借助Fourier分析方法对差分格式的稳定性进行了分析,并讨论了差分格式的误差和收敛性问题.A finite difference method and a convergence problem for a kind of anomalous diffusion equation with Neumann conditions are discussed. A finite difference scheme is obtained by adopting the method of the first-order forward difference quotient and second-order space center difference quotient and the formula of higher-order linear multistep method to discrete the fractional derivatives. The stability of the difference scheme is analyzed by means of Fourier analysis and the errors and convergence of the schemes are also discussed.

关 键 词：反常次扩散方程 差分法 分离变量法 

分 类 号：O241.82[理学—计算数学]