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

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 deriva...

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Autores principales: Khan, Muhammad Asim, Alias, Norma, Khan, Ilyas, Salama, Fouad Mohammad, Eldin, Sayed M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9883294/
https://www.ncbi.nlm.nih.gov/pubmed/36707653
http://dx.doi.org/10.1038/s41598-023-28741-7
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author Khan, Muhammad Asim
Alias, Norma
Khan, Ilyas
Salama, Fouad Mohammad
Eldin, Sayed M.
author_facet Khan, Muhammad Asim
Alias, Norma
Khan, Ilyas
Salama, Fouad Mohammad
Eldin, Sayed M.
author_sort Khan, Muhammad Asim
collection PubMed
description 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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spelling pubmed-98832942023-01-29 A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation Khan, Muhammad Asim Alias, Norma Khan, Ilyas Salama, Fouad Mohammad Eldin, Sayed M. Sci Rep Article 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. Nature Publishing Group UK 2023-01-27 /pmc/articles/PMC9883294/ /pubmed/36707653 http://dx.doi.org/10.1038/s41598-023-28741-7 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Khan, Muhammad Asim
Alias, Norma
Khan, Ilyas
Salama, Fouad Mohammad
Eldin, Sayed M.
A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation
title A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation
title_full A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation
title_fullStr A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation
title_full_unstemmed A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation
title_short A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation
title_sort new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional cable equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9883294/
https://www.ncbi.nlm.nih.gov/pubmed/36707653
http://dx.doi.org/10.1038/s41598-023-28741-7
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