探讨二维变空间分数阶扩散方程,应用改进了的Grunwald-Letnikov分数阶导数定义对方程进行离散,建立了隐式差分格式,并给出数值算例。进一步讨论由最终时刻观测数据确定微分阶数的反问题,并应用同伦正则化算法进行数值反演模拟。
An implicit finite difference scheme is introduced to solve the 2-D variable-order space diffusion equation,and an inverse problem of determining the variable fractional order is set forth using the additional measurements at the last minute.The homotopy regularization algorithm is applied to solve the inverse problem,and numerical examples are presented.