Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretiz...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Public Library of Science (PLoS)
2014-01-01
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| Series: | PLoS ONE |
| Online Access: | http://europepmc.org/articles/PMC3888394?pdf=render |
| _version_ | 1819263852818202624 |
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| author | Muhammad Abbas Ahmad Abd Majid Ahmad Izani Md Ismail Abdur Rashid |
| author_facet | Muhammad Abbas Ahmad Abd Majid Ahmad Izani Md Ismail Abdur Rashid |
| author_sort | Muhammad Abbas |
| collection | DOAJ |
| description | In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions. |
| first_indexed | 2024-12-23T20:20:11Z |
| format | Article |
| id | doaj.art-fed4c184086943c38d2e800fe74027bb |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-23T20:20:11Z |
| publishDate | 2014-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-fed4c184086943c38d2e800fe74027bb2022-12-21T17:32:34ZengPublic Library of Science (PLoS)PLoS ONE1932-62032014-01-0191e8326510.1371/journal.pone.0083265Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.Muhammad AbbasAhmad Abd MajidAhmad Izani Md IsmailAbdur RashidIn this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.http://europepmc.org/articles/PMC3888394?pdf=render |
| spellingShingle | Muhammad Abbas Ahmad Abd Majid Ahmad Izani Md Ismail Abdur Rashid Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system. PLoS ONE |
| title | Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system. |
| title_full | Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system. |
| title_fullStr | Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system. |
| title_full_unstemmed | Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system. |
| title_short | Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system. |
| title_sort | numerical method using cubic b spline for a strongly coupled reaction diffusion system |
| url | http://europepmc.org/articles/PMC3888394?pdf=render |
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