Coimbra变时间分数阶扩散-波动方程的新隐式差分法

将一阶的时间偏导数用Coimbra变时间分数阶导数算子进行替换,提出了一种新隐式差分解法.首先,对Coimbra型变时间分数阶导数算子和二阶空间导数进行离散化处理,将Coimbra变时间分数阶扩散-波动方程转化为代数方程组求解;然后,借助于数学归纳法给出了新隐式差分方法的收敛性分析,并证明了新隐式差分方法是无条件收敛的;最后,通过数值例子检验该方法,计算结果表明新隐式差分方法的理论分析是正确的,所构造的离散格式是可行的和有效的.

On a New Implicit Difference Method for Coimbra Variable Order Time Fractional Diffusion_Wave Equation

In this paper ,a Coimbra variable order time fractional diffusion_wave equation has been consid_ered ,in w hich the first order derivative is replaced by a Coimbra variable order time fractional derivative operator ,and a new implicit difference method is given .Firstly ,the Coimbra variable order time fractional derivative and the second order space derivative is discretized and used to transform the Coimbra variable order time fractional diffusion_wave into a system of algebraic equations .Then ,the convergence of the new implicit difference method has been discussed by mathematical induction ,and it proves that the meth_od is unconditional stable .Finally ,a numerical example show s that the numerical analysis is right and the method is feasible and efficient .