一类变时间分数阶扩散方程的数值计算方法  

Numerical Method for a Class of Variable Time Fractional Diffusion Equation

作　　者：刘建平[1] 张晴 毛学志[1] LIU Jianping, ZHANG Qing, MAO Xuezhi(School of Mathematics and Information Science ＆ Technology, Hebei Normal University ofScience ＆ Technology, Qinhuangdao Hebei,066004,Chin)

机构地区：[1]河北科技师范学院数学与信息科技学院,河北秦皇岛066004

出　　处：《河北科技师范学院学报》2018年第2期22-27,共6页Journal of Hebei Normal University of Science & Technology

基　　金：河北省青年自然科学基金项目(项目编号:A2015407063)

摘　　要：考虑移位勒让德多项式的正交性及可计算性,在Caputo类型的变分数阶微分定义下,给出了移位勒让德多项式的微分算子矩阵。然后,利用得到的算子矩阵将变时间分数阶扩散方程转化成可利用最小二乘法求解的线性方程组。最后,通过数值算例验证了该算法的有效性及正确性。Considering the orthogonality and calculability of the shifted Legendre polynomials,the differential operator matrix of shifted Legendre polynomials is given for the variable fractional order differential with definition of Caputo type. Using the obtained operator matrix,the variable time fractional diffusion equation is transformed into a linear system,which can be solved by least square method. A numerical example is given to illustrate the effectiveness and correctness of the proposed method.

关 键 词：变分数阶导数 移位勒让德多项式 微分算子矩阵 变时间分数阶扩散方程 

分 类 号：O241.4[理学—计算数学]