时间分数阶扩散方程的二阶差分/拟小波法  

Second order difference/quasi-wavelet method for the time fractional diffusion equation

作　　者：郭冲 赵凤群[1] GUO Chong;ZHAO Feng-qun(School of Sciences,Xi′an University of Technology,Xi′an 710054,China)

机构地区：[1]西安理工大学理学院,陕西西安710054

出　　处：《陕西科技大学学报》2019年第3期179-184,共6页Journal of Shaanxi University of Science & Technology

基　　金：陕西省科技厅工业科技攻关计划项目(2015GY004)

摘　　要：为了研究时间分数阶扩散方程的高精度的数值方法,得到高阶的数值格式,采用Caputo分数阶导数的差分公式——L2-1_σ公式离散时间分数阶导数,得到了时间分数阶扩散方程的半离散格式,并证明了半离散格式是无条件稳定的,且收敛阶为O(τ~2).空间导数采用拟小波方法离散,构造出了时间分数阶扩散方程的一种新的全离散数值格式.最后,通过数值算例验证了理论分析的正确性和数值解的有效性,而且结果表明这种算法收敛快、误差小,是一种高效的数值算法.In order to study the high-precision numerical method of the time fractional diffusion equation,the high-order numerical scheme is obtained.By using the difference formula of Caputo fractional derivative--L2-1σformula to discrete the time fractional derivative,the time semi-discrete scheme of the time fractional diffusion equation is obtained,it is proved that the semi-discrete scheme is unconditionally stable and convergence with O(τ2).The quasi-wavelet method is used to discretize the spatial derivative,then a new fully discrete numerical scheme for the time fractional diffusion equation is constructed.Finally,numerical examples are given to verify the correctness of the theoretical analysis and the validity of the numerical solution.It is also shown that the proposed algorithm has fast convergence and small error,and it is an efficient numerical algorithm.

关 键 词：时间分数阶扩散方程 L2-1σ公式 拟小波法 稳定性 

分 类 号：O241.82[理学—计算数学]