In this article, we develop fourth-order compact difference schemes based on the linearized generalized BDF2-θ to solve the two-dimensional nonlinear fractional mobile/immobile (M/I) transport equations. We derive theoretical results, including unconditional stability and error estimates associated with solution regularity. Finally, we provide extensive numerical examples with smooth solutions to demonstrate the effectiveness and accuracy of the schemes and develop the corrected compact difference scheme to recovery convergence results with nonsmooth solutions.

中文翻译：

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二维非线性分数移动/固定传输模型的四阶紧致差分格式

在本文中，我们开发了基于线性化广义 BDF2- θ 的四阶紧致差分格式来求解二维非线性分数移动/不动 (M/I) 传输方程。我们推导出理论结果，包括与解决方案规律性相关的无条件稳定性和误差估计。最后，我们提供了大量带有平滑解的数值例子来证明这些方案的有效性和准确性，并开发了修正的紧凑差分方案以恢复非平滑解的收敛结果。