时间分数阶扩散方程有限体积法的隐式差分格式  

Implicit Difference Scheme for Finite Volume Method of Time Fractional Diffusion Equation

作　　者：郑达艺[1] 陈柳娟[1] ZHENG Dayi;CHEN Liujuan(Department of Mathematics,Fujian Institute of Education,Fuzhou,Fujian 350025)

机构地区：[1]福建教育学院数学研修部,福建福州350001

出　　处：《武夷学院学报》2023年第3期34-37,52,共5页Journal of Wuyi University

基　　金：福建省自然科学基金资助项目(2019J01783);福建省教育厅中青年教师教育科研项目(科技类)(JAT201525)。

摘　　要：对于时间Caputo型导数的扩散方程,根据Caputo型导数和Grunwald-Letnikov型导数的关系,利用Grunwald-Letnikov型导数的离散格式离散分数阶导数,构造有限体积法的隐式差分格式,并证明差分格式的无条件稳定性和无条件收敛性,并给出数值例子。For the diffusion equation with time Caputo type derivatives,based on the relationship between Caputo type derivatives and Grunwald-letnikov type derivatives,an implicit difference scheme for the finite volume method is constructed by using the discrete scheme of Grunwald-letnikov type derivatives to discretize fractional derivatives.The unconditional stability and unconditional convergence of the difference scheme are proved,and numerical examples are given.

关 键 词：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]