基于L2-1σ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 L2-1σ scheme
姜楠楠 1周晓军1
作者信息
- 1. 贵州师范大学数学科学学院,贵州贵阳 550025
- 折叠
摘要
针对时间分数阶扩散方程,在时间方向上结合L2-1σ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I2-1σ格式和L1格式进行了误差和收敛阶的对比,显示出L2-1σ格式在时间分数阶导数逼近上的优势.
Abstract
The time fractional diffusion equation is combined with the L2-1σ scheme in the time direc-tion,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 meth-od 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 L2-1σ scheme and the L1 scheme,which shows the superiority of the L2-1σ 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Key words
time fractional diffusion equation/convergence order/difference scheme引用本文复制引用
基金项目
国家自然科学基金资助项目(12061023)
出版年
2024
NETL
NSTL
万方数据