Midpoint splitting methods for nonlinear space fractional diffusion equations

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 Gr & uuml;nwald 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.