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. 2023 Jan 27;13(1):1549.
doi: 10.1038/s41598-023-28741-7.

A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation

Muhammad Asim Khan  1 , Norma Alias  2 , Ilyas Khan  3 , Fouad Mohammad Salama  4 , Sayed M Eldin  5
Affiliations

A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation

Muhammad Asim Khan et al. Sci Rep. .

Abstract

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.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Grid points for the proposed scheme (8).
Figure 2
Figure 2
Computational molecule for the proposed scheme (7).
Figure 3
Figure 3
The Example 1 absolute error, when h=τ=125 and γ=0.1.
Figure 4
Figure 4
The Example 2 absolute error when h=τ=125 and γ=0.1.
Figure 5
Figure 5
Analytical and numerical solution for example 1, when h=τ=125.
Figure 6
Figure 6
Analytical and numerical solution for example 1, when h=τ=125.
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