Numerical Solution for Sine-Gordon System in One Dimension
This paper has studied the numerical solution for Sine-Gordon system in one dimensions using finite difference methods. We have used Explicit method and Crank-Nicholson method.A comparison between results of the two methods has been done and we obtained that Crank-Nicholson method is more accurate t...
| Main Authors: | , |
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| Format: | Article |
| Language: | Arabic |
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Mosul University
2010-12-01
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| Series: | Al-Rafidain Journal of Computer Sciences and Mathematics |
| Subjects: | |
| Online Access: | https://csmj.mosuljournals.com/article_163896_6371e014bd9e9f9c419513fa9c39d2f3.pdf |
| _version_ | 1811265723107901440 |
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| author | Saad Manna Haneen Jassim |
| author_facet | Saad Manna Haneen Jassim |
| author_sort | Saad Manna |
| collection | DOAJ |
| description | This paper has studied the numerical solution for Sine-Gordon system in one dimensions using finite difference methods. We have used Explicit method and Crank-Nicholson method.A comparison between results of the two methods has been done and we obtained that Crank-Nicholson method is more accurate than the Explicit method but the Explicit method is easer .
We also studied the stability analysis for each method by using Fourier(Von-Neumann) method and obtained that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the condition and . |
| first_indexed | 2024-04-12T20:27:53Z |
| format | Article |
| id | doaj.art-1581b06b18d54261a9a47432dfc4350d |
| institution | Directory Open Access Journal |
| issn | 1815-4816 2311-7990 |
| language | Arabic |
| last_indexed | 2024-04-12T20:27:53Z |
| publishDate | 2010-12-01 |
| publisher | Mosul University |
| record_format | Article |
| series | Al-Rafidain Journal of Computer Sciences and Mathematics |
| spelling | doaj.art-1581b06b18d54261a9a47432dfc4350d2022-12-22T03:17:48ZaraMosul UniversityAl-Rafidain Journal of Computer Sciences and Mathematics1815-48162311-79902010-12-0172475910.33899/csmj.2010.163896163896Numerical Solution for Sine-Gordon System in One DimensionSaad Manna0Haneen Jassim1College of Education University of Dohuk, IraqCollege of Computer Science and Mathematics University of Mosul, Mosul, IraqThis paper has studied the numerical solution for Sine-Gordon system in one dimensions using finite difference methods. We have used Explicit method and Crank-Nicholson method.A comparison between results of the two methods has been done and we obtained that Crank-Nicholson method is more accurate than the Explicit method but the Explicit method is easer . We also studied the stability analysis for each method by using Fourier(Von-Neumann) method and obtained that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the condition and .https://csmj.mosuljournals.com/article_163896_6371e014bd9e9f9c419513fa9c39d2f3.pdfsine-gordon systemfinite difference methodsexplicit methodcrank-nicholson methodstability analysisfourier(von-neumann) method |
| spellingShingle | Saad Manna Haneen Jassim Numerical Solution for Sine-Gordon System in One Dimension Al-Rafidain Journal of Computer Sciences and Mathematics sine-gordon system finite difference methods explicit method crank-nicholson method stability analysis fourier(von-neumann) method |
| title | Numerical Solution for Sine-Gordon System in One Dimension |
| title_full | Numerical Solution for Sine-Gordon System in One Dimension |
| title_fullStr | Numerical Solution for Sine-Gordon System in One Dimension |
| title_full_unstemmed | Numerical Solution for Sine-Gordon System in One Dimension |
| title_short | Numerical Solution for Sine-Gordon System in One Dimension |
| title_sort | numerical solution for sine gordon system in one dimension |
| topic | sine-gordon system finite difference methods explicit method crank-nicholson method stability analysis fourier(von-neumann) method |
| url | https://csmj.mosuljournals.com/article_163896_6371e014bd9e9f9c419513fa9c39d2f3.pdf |
| work_keys_str_mv | AT saadmanna numericalsolutionforsinegordonsysteminonedimension AT haneenjassim numericalsolutionforsinegordonsysteminonedimension |