两项时间分数阶扩散方程的一种数值解法  

A numerical solution of two-term time fractional diffusion equations

作　　者：余跃玉 YU Yue-yu(School of Mathematics,Sichuan University of Arts and Sciences,Dazhou 635000,Sichuan,China)

机构地区：[1]四川文理学院数学学院,四川达州635000

出　　处：《西北师范大学学报（自然科学版）》2023年第5期19-23,共5页Journal of Northwest Normal University(Natural Science)

基　　金：四川省高等教育人才培养质量和教学改革项目(JG2021-1362);达州市数学与金融研究中心2022年度开放课题项目(SCMF202209);四川文理学院一流课程建设项目(2021KCB010)。

摘　　要：扩散方程在物理领域常用来模拟不同物质间的相互扩散现象,多项时间分数阶扩散方程能更清晰地反应复杂系统的物理意义.本文对两项时间分数阶扩散方程中的分数阶导数直接进行离散,空间导数采用中心差分格式进行离散,提出了求解两项时间分数阶扩散方程的一个隐式差分格式;讨论了分数阶扩散方程差分解的存在唯一性,证明了差分格式的稳定性及收敛性;最后数值试验验证了格式的有效性.The diffusion equation is often used to simulate the mutual diffusion between different substances in a physical field,and the multi-term time fractional diffusion equation can more clearly reflect the physical meaning of complex systems.In this paper,the fractional derivative of the two-term time fractional diffusion equation is discretized directly,and the spatial derivative is discretized by the central difference scheme.An implicit difference scheme is proposed to solve the two-term time fractional diffusion equation.Then existence and uniqueness of the difference solution for this equation are discussed,and the stability and convergence of the difference scheme are also proved.Finally,numerical experiments verify the effectiveness of this scheme.

关 键 词：扩散方程 分数阶导数 隐式差分格式 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]