基于L2-1_(σ)格式逼近时间分数阶扩散方程的差分方法及其收敛性分析  

Difference method and its convergence analysis for time-fractional diffusion equation based on L2-1_(σ)scheme

作　　者：姜楠楠 周晓军 JIANG Nannan;ZHOU Xiaojun(School of Mathematical Science,Guizhou Normal University,Guiyang,Guizhou 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《贵州师范大学学报（自然科学版）》2024年第2期100-105,111,共7页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(12061023)。

摘　　要：针对时间分数阶扩散方程,在时间方向上结合L2-1_(σ)格式,空间上采用二阶中心差分方法进行离散,并对离散格式进行了收敛性和稳定性分析,离散格式和分析方法可以很容易推广到空间高维情形。最后,通过数值算例对L2-1_(σ)格式和L1格式进行了误差和收敛阶的对比,显示出L2-1_(σ)格式在时间分数阶导数逼近上的优势。The time fractional diffusion equation is combined with the L2-1_(σ)scheme in the time direction,and the second order central difference method is used to discretization in space.The convergence and stability of the discretization scheme are analyzed.The discretization scheme and the analysis method can be easily extended to the case of high dimensional space.Finally,a numerical example is given to compare the error and convergence order of the L2-1_(σ)scheme and the L1 scheme,which shows the superiority of the L2-1_(σ)scheme in time fractional derivative approximation.

关 键 词：时间分数阶扩散方程 收敛阶 差分格式 

分 类 号：O241.8[理学—计算数学]