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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| Format: | Article |
| Language: | English |
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EJAAM
2024-12-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
| Subjects: | |
| Online Access: | https://ejaam.org/articles/2024/10.62780-ejaam-2024-005.pdf |
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| Summary: | 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. |
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| ISSN: | 2544-9990 |