变分数阶扩散方程的新隐式差分法  

A new implicit difference method for the variable order fractional diffusion equation

作　　者：于春肖[1] 苑润浩[1] 魏国勇[1] 崔栋[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《安徽大学学报（自然科学版）》2014年第1期12-18,共7页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11301459);河北省自然科学基金资助项目(A2011203020);河北省高等学校科学技术研究基金重点资助项目(ZD2010116)

摘　　要：针对变分数阶扩散方程,提出新隐式差分法.首先,对二阶空间导数和Riemann-Liouville型变时间分数阶导数算子进行离散化处理,将变分数阶扩散方程转化为代数方程组求解;然后,借助Fourier级数技术给出了新隐式差分法的收敛性分析;最后,通过数值算例检验该方法,计算结果表明了新隐式差分法的可行性和有效性.A new implicit numerical difference method was proposed for the variable order fractional diffusion equation. Firstly, the second-order space derivative and the fractional-order time derivative could be discretized and used to transform the variable order fractional diffusion equation into a system of algebraic equations. Then, the convergence of the numerical method was discussed by Fourier analysis. Finally, some numerical examples were provided to test this method and the results demonstrated the feasibility and the efficiency of the proposed method.

关 键 词：变分数阶扩散方程 新隐式差分法 变时间分数阶导数算子 收敛性分析 

分 类 号：O242[理学—计算数学]