求解一类多项四阶时间分数阶慢扩散系统的有限差分格式

A Finite Difference Scheme for Solving A Class of Multi-term Time Fractional Sub-diffusion System with the Spatial Fourth-order Derivative

介绍求解多项四阶时间分数阶慢扩散方程的有限差分方法.利用L1公式逼近时间分数阶导数,用降阶法处理空间四阶导数项,再借助离散能量方法证明差分格式是无条件稳定的且在无穷范数下其收敛阶为O(τ2-β+h2),其中τ和h分别为时间方向和空间方向的步长,β是时间分数导数的最大阶.最后用数值实验验证所提出差分格式的精度和有效性.

A finite difference scheme is derived for solving a class of multi-term time fractional sub-diffusion system with the spatial fourth-order derivative,where the L1 formula is used to approximate the time fractional derivatives and using the method of order reduction to deal with the spatial fourth-order derivative.Taking the discrete energy method,the unconditional stability and convergence of the scheme are proved and the convergence order is O(τ^2-β+h^2)in L∞-norm,whereτand h are temporal step size and spatial step size respectively.βis the maximum order of time fractional derivatives.Finally,a numerical example is demonstrated to show the accuracy and efficiency of the present method.