一类分数阶时滞扩散微分方程的数值解法

A Numerical Method for Solving Certain Fractional Diffusion Differential Equations with Delay

考虑了一类时间分数阶变系数时滞扩散微分方程,方程中对时间的导数由传统一阶导数变为α(0<α<1)阶导数,对此类方程利用差分法构造了有效的差分格式,并对此格式的收敛性和稳定性进行证明,数值算例检验该格式解决此类方程是有效的.

A numerical method is presented to solve one kind of time fractional variable coefficients delay diffusion differential equation,the first-order time derivative is replaced by Caputo fractional derivative,and a difference scheme is given,the difference scheme is stable and convergence.Numerical example shows that the numerical method is a practical method.