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Azami, Leyla, Refahi Sheikhani, Amir Hosein, Saberi Najafi, Hashem. (1401). A numerical method based on finite difference scheme for solving fractional Cable equation. , (), -. doi: 10.30495/jnrm.2022.63486.2153
Leyla Azami; Amir Hosein Refahi Sheikhani; Hashem Saberi Najafi. "A numerical method based on finite difference scheme for solving fractional Cable equation". , , , 1401, -. doi: 10.30495/jnrm.2022.63486.2153
Azami, Leyla, Refahi Sheikhani, Amir Hosein, Saberi Najafi, Hashem. (1401). 'A numerical method based on finite difference scheme for solving fractional Cable equation', , (), pp. -. doi: 10.30495/jnrm.2022.63486.2153
Azami, Leyla, Refahi Sheikhani, Amir Hosein, Saberi Najafi, Hashem. A numerical method based on finite difference scheme for solving fractional Cable equation. , 1401; (): -. doi: 10.30495/jnrm.2022.63486.2153

A numerical method based on finite difference scheme for solving fractional Cable equation

Journal of New Researches in Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 آذر 1401  XML
نوع مقاله: research paper
شناسه دیجیتال (DOI): 10.30495/jnrm.2022.63486.2153
نویسندگان
Leyla Azami1؛ Amir Hosein Refahi Sheikhani email orcid 2؛ Hashem Saberi Najafiorcid 1
1Department of Applied Mathematics, Faculty of Mathematics Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran
2Department of Applied Mathematics,Faculty of Mathematical Sciences,Lahidjan Branch, Islamic Azad University,Lahijan,Iran
چکیده
In this paper, we proposed a numerical approximation to solve a type of fractional Cable equations based on the finite difference scheme that can be easily generalized to other fractional cable equations. The fractional derivatives are considered in the Caputo-Fabrizio type. By using the forward difference formula, the fractional derivative is approximated and then we can discretize the fractional equation with the mentioned approximation and difference scheme In order to demonstrate the stability and convergence, several Theorems and Lemmas are provided. Finally, two numerical examples of the cable equation with different boundary and initial conditions are used to demonstrate the effective and accuracy of the scheme. The obtained numerical results are compared with the analytical solution. Figures presented in both examples show consistency of numerical and analytical solutions that can be clearly seen. Tables also show a small error between the numerical and analytical solution which show that our proposed method is highly accurate.
کلیدواژه‌ها
Membrane potential؛ Caputo-Fabrizio derivative؛ Fourier analysis؛ Stability؛ Convergence
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تعداد مشاهده مقاله: 84


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