In this paper, the Crank–Nicolson (CN) and rotated four-point fractional explicit decoupled group (EDG) methods are introduced to solve the two-dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the and axes. The local truncation error of CN and EDG is presented. Also, the stability and convergence of the proposed methods are proved. Some numerical experiments are performed to show the efficiency of the presented methods in terms of accuracy and CPU time.

中文翻译：

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二维分数阶Burgers方程的有效显式解耦组方法及其收敛性分析

在本文中，引入了Crank-Nicolson（CN）和旋转四点分数显式解耦组（EDG）方法来求解二维时间-分数阶Burgers方程。EDG方法是通过泰勒展开和Crank–Nicolson方法绕和轴旋转45°得出的。给出了CN和EDG的局部截断误差。同时，证明了所提方法的稳定性和收敛性。进行了一些数值实验，以显示所提方法在准确性和CPU时间方面的效率。