Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods
This paper aims to propose the semi implicit finite difference method for discretizing Cahn-Allen equation. The stability and convergence analysis are proved. It is shown that the suggest scheme is stable for the usage of the Fourier-Von Neumann technique. The accuracy of the proposed method is firs...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Tishk International University
2022-06-01
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| Series: | Eurasian Journal of Science and Engineering |
| Subjects: | |
| Online Access: | https://eajse.tiu.edu.iq/index.php/volume-8-issue-1-article-8/ |
| _version_ | 1797761834141351936 |
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| author | Younis A. Sabawi Supa B. Ahmed Hoshman Q. Hamad |
| author_facet | Younis A. Sabawi Supa B. Ahmed Hoshman Q. Hamad |
| author_sort | Younis A. Sabawi |
| collection | DOAJ |
| description | This paper aims to propose the semi implicit finite difference method for discretizing Cahn-Allen equation. The stability and convergence analysis are proved. It is shown that the suggest scheme is stable for the usage of the Fourier-Von Neumann technique. The accuracy of the proposed method is first order in time and second order in space. A comparison between the numerical and the exact solutions is supported with two examples. Numerical results are shown that there is a good agreement between the approximate solution and exact solution. |
| first_indexed | 2024-03-12T19:19:44Z |
| format | Article |
| id | doaj.art-3dd0c4e6b2db4e1183f4267d16a480b5 |
| institution | Directory Open Access Journal |
| issn | 2414-5629 2414-5602 |
| language | English |
| last_indexed | 2024-03-12T19:19:44Z |
| publishDate | 2022-06-01 |
| publisher | Tishk International University |
| record_format | Article |
| series | Eurasian Journal of Science and Engineering |
| spelling | doaj.art-3dd0c4e6b2db4e1183f4267d16a480b52023-08-02T05:16:37ZengTishk International UniversityEurasian Journal of Science and Engineering2414-56292414-56022022-06-01819010010.23918/eajse.v8i1p90Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference MethodsYounis A. Sabawi0 Supa B. Ahmed1Hoshman Q. Hamad2Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Koya, Iraq & Mathematics Education Department, Faculty of Education, Tishk International University, Erbil, IraqMathematics Education Department, Faculty of Education, Tishk International University, Erbil, IraqDepartment of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Koya, IraqqThis paper aims to propose the semi implicit finite difference method for discretizing Cahn-Allen equation. The stability and convergence analysis are proved. It is shown that the suggest scheme is stable for the usage of the Fourier-Von Neumann technique. The accuracy of the proposed method is first order in time and second order in space. A comparison between the numerical and the exact solutions is supported with two examples. Numerical results are shown that there is a good agreement between the approximate solution and exact solution.https://eajse.tiu.edu.iq/index.php/volume-8-issue-1-article-8/allen equationsemi implicit finite differencestability of allen equation |
| spellingShingle | Younis A. Sabawi Supa B. Ahmed Hoshman Q. Hamad Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods Eurasian Journal of Science and Engineering allen equation semi implicit finite difference stability of allen equation |
| title | Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods |
| title_full | Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods |
| title_fullStr | Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods |
| title_full_unstemmed | Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods |
| title_short | Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods |
| title_sort | numerical treatment of allen s equation using semi implicit finite difference methods |
| topic | allen equation semi implicit finite difference stability of allen equation |
| url | https://eajse.tiu.edu.iq/index.php/volume-8-issue-1-article-8/ |
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