We propose a midpoint splitting method to solve nonlinear space fractional diffusion equations. We first discretize the equation in space using the weighted and shifted Grünwald difference (WSGD) operators. Then, we obtain the fully discrete scheme of the equation using the midpoint splitting method, which can alleviate computational costs and mitigate instability issues that may arise. We establish the stability result of the fully discrete scheme under certain conditions. Finally, we demonstrate its feasibility and efficiency through numerical examples.

中文翻译：

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非线性空间分数扩散方程的中点分裂方法

我们提出了一种中点分裂方法来求解非线性空间分数扩散方程。我们首先使用加权和移位 Grünwald 差分 (WSGD) 算子在空间中离散方程。然后，我们使用中点分裂方法获得方程的完全离散格式，这可以减轻计算成本并减轻可能出现的不稳定问题。我们建立了全离散方案在一定条件下的稳定性结果。最后，我们通过数值例子证明了其可行性和效率。