In this article, we consider an anomalous diffusion model in a planar polymeric matrix as a space fractional diffusion problem with moving boundary conditions. An iterative implicit finite difference method with variable time‐steps is established to solve the proposed problem. The stability and consistency of the numerical method are proved and the estimation of the numerical error is conducted. The numerical results are compared with the scale‐invariant and homotopy perturbation solutions when the diffusion coefficient is a constant. Furthermore, the numerical results for a test case with time‐dependent diffusion coefficient are reported.

中文翻译：

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空间分数扩散移动边界问题的可变时步方法：在平面药物释放装置中的应用

在本文中，我们将平面聚合物基体中的反常扩散模型视为具有移动边界条件的空间分数扩散问题。建立了具有可变时间步长的迭代隐式有限差分方法来解决所提出的问题。证明了数值方法的稳定性和一致性，并对数值误差进行了估计。当扩散系数为常数时，将数值结果与尺度不变和同伦摄动解进行比较。此外，还报告了具有随时间变化的扩散系数的测试案例的数值结果。