一个分数阶扩散方程的定解问题的数值解法

A Numerical Method for the Solution of a Fractional Diffusion Equation

研究了一个扩散系数与空间变量相关的一维空间-时间分数阶扩散方程的定解问题。基于Riemann-Liouville意义下空间导数和Caputo意义下时间导数的离散,提出了一种求解方程的隐式差分格式,验证了这个格式是无条件稳定,并证明了它的收敛性,其收敛的阶为O(τ+h),最后给出了数值例子。

The solution of a space-time fractional diffusion equation with spale deperdent diffusion coefficient is studied. An implicit difference scheme is presented based on the dispersion of the space derivatives in sense of Rimmann-Liouville and the time derivatives in sense of Caputo. The format is tested to be unconditional stable and its astringency is proved. The result shows convergence order of the method is O （ τ ＋ h）. Finally, the numerical example is given.