Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems
This paper presents the existence and uniqueness of the weak solution for the nonlinear system of sine-Gordon equations which describes DNA dynamics. An unconditionally stable second order difference scheme generated by the unbounded operator A2 corresponding to the system of sine-Gordon equations i...
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EJAAM
2024-12-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2024/10.62780-ejaam-2024-005.pdf |
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| author | Ozgur Yildirim |
| author_facet | Ozgur Yildirim |
| author_sort | Ozgur Yildirim |
| collection | DOAJ |
| description | This paper presents the existence and uniqueness of the weak solution for the nonlinear system of sine-Gordon equations which describes DNA dynamics. An unconditionally stable second order difference scheme generated by the unbounded operator A2 corresponding to the system of sine-Gordon equations is considered. Weak solutions are a more general type of solution to the system of sine-Gordon equations than classical solutions and are important in the case of low regularity conditions. The weak solvability is studied in the space of distributions using variational methods. A very efficient numerical method that combines the finite difference method and the fixed point theory is used to perform numerical experiments to verify theoretical statements. |
| format | Article |
| id | doaj-art-99ba7e0af00d47eda9dc9b1378f23cbd |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-99ba7e0af00d47eda9dc9b1378f23cbd2025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902024-12-01202410.62780/ejaam/2024-005Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systemsOzgur Yildirim0Department of Mathematics, Yildiz Technical University, 34220, Istanbul, Türkiye & Department of Mathematics, Bahcesehir University, 34353, Istanbul, Türkiye.This paper presents the existence and uniqueness of the weak solution for the nonlinear system of sine-Gordon equations which describes DNA dynamics. An unconditionally stable second order difference scheme generated by the unbounded operator A2 corresponding to the system of sine-Gordon equations is considered. Weak solutions are a more general type of solution to the system of sine-Gordon equations than classical solutions and are important in the case of low regularity conditions. The weak solvability is studied in the space of distributions using variational methods. A very efficient numerical method that combines the finite difference method and the fixed point theory is used to perform numerical experiments to verify theoretical statements.https://ejaam.org/articles/2024/10.62780-ejaam-2024-005.pdfexistenceuniquenessweak solutionsdifference schemesstability |
| spellingShingle | Ozgur Yildirim Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems E-Journal of Analysis and Applied Mathematics existence uniqueness weak solutions difference schemes stability |
| title | Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems |
| title_full | Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems |
| title_fullStr | Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems |
| title_full_unstemmed | Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems |
| title_short | Weak solutions of unconditionally stable second-order difference schemes for nonlinear sine-Gordon systems |
| title_sort | weak solutions of unconditionally stable second order difference schemes for nonlinear sine gordon systems |
| topic | existence uniqueness weak solutions difference schemes stability |
| url | https://ejaam.org/articles/2024/10.62780-ejaam-2024-005.pdf |
| work_keys_str_mv | AT ozguryildirim weaksolutionsofunconditionallystablesecondorderdifferenceschemesfornonlinearsinegordonsystems |