In this paper, we propose a second-order finite difference scheme to study a class of space–time variable-order fractional diffusion equation, and show that the scheme is not only unconditionally stable but also convergent with the convergence order $O({\tau }^2+h^2)$ under certain conditions. Some numerical examples are illustrated which are in good agreement with our theoretical results.

中文翻译：

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时空变数扩散方程的二阶数值方法

本文提出了一种二阶有限差分方案，研究了一类时空变分分数阶扩散方程，证明了该方案不仅无条件稳定，而且收敛于收敛阶。 $Ø（{\tau }^2+H^2）$在某些条件下。给出了一些数值例子，这些例子与我们的理论结果非常吻合。