Numerical Solution of Time Fractional Cable Equation via the Sinc-Bernoulli Collocation Method
An important equation usually used in modeling neuronal dynamics is cable equation. In this work, a numerical method for the fractional cable equation which involves two Riemann-Liouville fractional derivatives is proposed. Our computational technique is based on collocation idea where a combination...
| 发表在: | Journal of Applied and Computational Mechanics |
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| Main Authors: | , |
| 格式: | 文件 |
| 语言: | 英语 |
| 出版: |
Shahid Chamran University of Ahvaz
2021-10-01
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| 主题: | |
| 在线阅读: | https://jacm.scu.ac.ir/article_15318_34b03fdbad5545b18d79d846f7cb6fe1.pdf |
| _version_ | 1851923550711054336 |
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| author | Nasrin Moshtaghi Abbas Saadatmandi |
| author_facet | Nasrin Moshtaghi Abbas Saadatmandi |
| author_sort | Nasrin Moshtaghi |
| collection | DOAJ |
| container_title | Journal of Applied and Computational Mechanics |
| description | An important equation usually used in modeling neuronal dynamics is cable equation. In this work, a numerical method for the fractional cable equation which involves two Riemann-Liouville fractional derivatives is proposed. Our computational technique is based on collocation idea where a combination of Bernoulli polynomials and Sinc functions are used to approximate the solution to this problem. The constructed approximation by our method convert the fractional cable equation into a set of algebraic equations. Also, we provide two numerical examples to confirm the accuracy and effectiveness of the present method. |
| format | Article |
| id | doaj-art-e2d38e7b4f6f410888773de3178bca0d |
| institution | Directory of Open Access Journals |
| issn | 2383-4536 |
| language | English |
| publishDate | 2021-10-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| spelling | doaj-art-e2d38e7b4f6f410888773de3178bca0d2025-08-19T21:57:21ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362021-10-01741916192410.22055/jacm.2020.31923.194015318Numerical Solution of Time Fractional Cable Equation via the Sinc-Bernoulli Collocation MethodNasrin Moshtaghi0Abbas Saadatmandi1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, IranAn important equation usually used in modeling neuronal dynamics is cable equation. In this work, a numerical method for the fractional cable equation which involves two Riemann-Liouville fractional derivatives is proposed. Our computational technique is based on collocation idea where a combination of Bernoulli polynomials and Sinc functions are used to approximate the solution to this problem. The constructed approximation by our method convert the fractional cable equation into a set of algebraic equations. Also, we provide two numerical examples to confirm the accuracy and effectiveness of the present method.https://jacm.scu.ac.ir/article_15318_34b03fdbad5545b18d79d846f7cb6fe1.pdffractional cable equationbernoulli polynomialsriemann-liouville fractional derivativesinc functionnumerical solution |
| spellingShingle | Nasrin Moshtaghi Abbas Saadatmandi Numerical Solution of Time Fractional Cable Equation via the Sinc-Bernoulli Collocation Method fractional cable equation bernoulli polynomials riemann-liouville fractional derivative sinc function numerical solution |
| title | Numerical Solution of Time Fractional Cable Equation via the Sinc-Bernoulli Collocation Method |
| title_full | Numerical Solution of Time Fractional Cable Equation via the Sinc-Bernoulli Collocation Method |
| title_fullStr | Numerical Solution of Time Fractional Cable Equation via the Sinc-Bernoulli Collocation Method |
| title_full_unstemmed | Numerical Solution of Time Fractional Cable Equation via the Sinc-Bernoulli Collocation Method |
| title_short | Numerical Solution of Time Fractional Cable Equation via the Sinc-Bernoulli Collocation Method |
| title_sort | numerical solution of time fractional cable equation via the sinc bernoulli collocation method |
| topic | fractional cable equation bernoulli polynomials riemann-liouville fractional derivative sinc function numerical solution |
| url | https://jacm.scu.ac.ir/article_15318_34b03fdbad5545b18d79d846f7cb6fe1.pdf |
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