Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
Sci Rep. 2023 Jan 27;13(1):1549. doi: 10.1038/s41598-023-28741-7.
In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE). In the new proposed FDIS, the time fractional and space derivatives are discretized using the Caputo fractional derivative and fourth-order implicit scheme, respectively. Moreover, the proposed scheme theoretical analysis (convergence and stability) is also discussed using the Fourier analysis method. Finally, some numerical test problems are presented to show the effectiveness of the proposed method.
在本文中，我们为二维（2-D）时间分数 Cable 方程（FCE）的求解开发了一种新的高阶隐式有限差分迭代方案（FDIS）。在新提出的 FDIS 中，时间分数导数和空间导数分别采用 Caputo 分数导数和四阶隐式格式离散化。此外，还使用傅里叶分析方法讨论了所提出方案的理论分析（收敛性和稳定性）。最后，提出了一些数值测试问题以显示所提出方法的有效性。
