Using Crank-Nicolson Numerical Method to solve Heat-Diffusion Problem
The current study aimed to use the Crank-Nicolson numerical method to solve Heat-Diffusion Problem in comparison with the ADI method. In this paper, the general formula of the Crank-Nicolson Numerical Method was derived and applied to solve the heat diffusion. The same problem then has been solved...
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| Format: | Article |
| Language: | English |
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Tikrit University
2023-06-01
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| Series: | Tikrit Journal of Pure Science |
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| Online Access: | https://tjpsj.org/index.php/tjps/article/view/1434 |
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| author | Omar Abdullah Ajeel Awni M. Gaftan |
| author_facet | Omar Abdullah Ajeel Awni M. Gaftan |
| author_sort | Omar Abdullah Ajeel |
| collection | DOAJ |
| description |
The current study aimed to use the Crank-Nicolson numerical method to solve Heat-Diffusion Problem in comparison with the ADI method. In this paper, the general formula of the Crank-Nicolson Numerical Method was derived and applied to solve the heat diffusion. The same problem then has been solved using ADI numerical method. The results of the Crank-Nicolson numerical method were compared with that of the ADI numerical method. The comparison results revealed that Crank-Nicolson is more accurate than the results of ADI at the initial steps of the problem solution.
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| format | Article |
| id | doaj-art-dfde81a8ef86494bae014f2af67f84c3 |
| institution | Kabale University |
| issn | 1813-1662 2415-1726 |
| language | English |
| publishDate | 2023-06-01 |
| publisher | Tikrit University |
| record_format | Article |
| series | Tikrit Journal of Pure Science |
| spelling | doaj-art-dfde81a8ef86494bae014f2af67f84c32025-08-20T03:28:59ZengTikrit UniversityTikrit Journal of Pure Science1813-16622415-17262023-06-0128310.25130/tjps.v28i3.1434Using Crank-Nicolson Numerical Method to solve Heat-Diffusion ProblemOmar Abdullah Ajeel0Awni M. Gaftan1Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, IraqDepartment of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq The current study aimed to use the Crank-Nicolson numerical method to solve Heat-Diffusion Problem in comparison with the ADI method. In this paper, the general formula of the Crank-Nicolson Numerical Method was derived and applied to solve the heat diffusion. The same problem then has been solved using ADI numerical method. The results of the Crank-Nicolson numerical method were compared with that of the ADI numerical method. The comparison results revealed that Crank-Nicolson is more accurate than the results of ADI at the initial steps of the problem solution. https://tjpsj.org/index.php/tjps/article/view/1434Crank-NicolsonNumerical MethodHeat-Diffusion equationAlternating Directions Implicit (ADI) method. |
| spellingShingle | Omar Abdullah Ajeel Awni M. Gaftan Using Crank-Nicolson Numerical Method to solve Heat-Diffusion Problem Tikrit Journal of Pure Science Crank-Nicolson Numerical Method Heat-Diffusion equation Alternating Directions Implicit (ADI) method. |
| title | Using Crank-Nicolson Numerical Method to solve Heat-Diffusion Problem |
| title_full | Using Crank-Nicolson Numerical Method to solve Heat-Diffusion Problem |
| title_fullStr | Using Crank-Nicolson Numerical Method to solve Heat-Diffusion Problem |
| title_full_unstemmed | Using Crank-Nicolson Numerical Method to solve Heat-Diffusion Problem |
| title_short | Using Crank-Nicolson Numerical Method to solve Heat-Diffusion Problem |
| title_sort | using crank nicolson numerical method to solve heat diffusion problem |
| topic | Crank-Nicolson Numerical Method Heat-Diffusion equation Alternating Directions Implicit (ADI) method. |
| url | https://tjpsj.org/index.php/tjps/article/view/1434 |
| work_keys_str_mv | AT omarabdullahajeel usingcranknicolsonnumericalmethodtosolveheatdiffusionproblem AT awnimgaftan usingcranknicolsonnumericalmethodtosolveheatdiffusionproblem |