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

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.