Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study
In this article, a hybrid numerical scheme based on Lucas and Fibonacci polynomials in combination with St�rmer?s method for the solution of Klein/Sinh-Gordon equations is proposed. Initially, the problem is transformed to a time-discrete form by using St�rmer?s technique. Then, with the help of Fib...
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American Institute of Mathematical Sciences
2025
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| author | Ali I. Ahmad I. |
| author2 | 57211855967 |
| author_facet | 57211855967 Ali I. Ahmad I. |
| author_sort | Ali I. |
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| collection | Institutional Repository |
| content_provider | Universiti Tenaga Nasional |
| content_source | UNITEN Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this article, a hybrid numerical scheme based on Lucas and Fibonacci polynomials in combination with St�rmer?s method for the solution of Klein/Sinh-Gordon equations is proposed. Initially, the problem is transformed to a time-discrete form by using St�rmer?s technique. Then, with the help of Fibonacci polynomials, we approximate the derivatives of the function. The suggested technique is validated to both one and two-dimensional problems. The resultant findings are compared with existing numerical solutions and presented in a tabular form. The comparison reveals the superior accuracy of the scheme. The numerical convergence of the scheme is computed in each example. ? 2024 the Author(s). |
| format | Article |
| id | my.uniten.dspace-36930 |
| institution | Universiti Tenaga Nasional |
| publishDate | 2025 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | my.uniten.dspace-369302025-03-03T15:45:52Z Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study Ali I. Ahmad I. 57211855967 57220824630 In this article, a hybrid numerical scheme based on Lucas and Fibonacci polynomials in combination with St�rmer?s method for the solution of Klein/Sinh-Gordon equations is proposed. Initially, the problem is transformed to a time-discrete form by using St�rmer?s technique. Then, with the help of Fibonacci polynomials, we approximate the derivatives of the function. The suggested technique is validated to both one and two-dimensional problems. The resultant findings are compared with existing numerical solutions and presented in a tabular form. The comparison reveals the superior accuracy of the scheme. The numerical convergence of the scheme is computed in each example. ? 2024 the Author(s). Final 2025-03-03T07:45:51Z 2025-03-03T07:45:51Z 2024 Article 10.3934/mmc.2024029 2-s2.0-85205027447 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85205027447&doi=10.3934%2fmmc.2024029&partnerID=40&md5=e8261e93a9474a89e57685ed99595b4a https://irepository.uniten.edu.my/handle/123456789/36930 4 3 361 373 American Institute of Mathematical Sciences Scopus |
| spellingShingle | Ali I. Ahmad I. Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study |
| title | Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study |
| title_full | Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study |
| title_fullStr | Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study |
| title_full_unstemmed | Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study |
| title_short | Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study |
| title_sort | applications of the nonlinear klein/sinh-gordon equations in modern physics: a numerical study |
| url_provider | http://dspace.uniten.edu.my/ |