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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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 |
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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). |
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57211855967 |
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57211855967 Ali I. Ahmad I. |
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Article |
| author |
Ali I. Ahmad I. |
| spellingShingle |
Ali I. Ahmad I. Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study |
| author_sort |
Ali I. |
| title |
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_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_sort |
applications of the nonlinear klein/sinh-gordon equations in modern physics: a numerical study |
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American Institute of Mathematical Sciences |
| publishDate |
2025 |
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1825816150242492416 |
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13.244413 |