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 Störmer's method for the solution of Klein/Sinh-Gordon equations is proposed. Initially, the problem is transformed to a time-discrete form by using Störmer's technique. Then, with the h...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-09-01
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| Series: | Mathematical Modelling and Control |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2024029 |
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| author | Ihteram Ali Imtiaz Ahmad |
| author_facet | Ihteram Ali Imtiaz Ahmad |
| author_sort | Ihteram Ali |
| collection | DOAJ |
| description | In this article, a hybrid numerical scheme based on Lucas and Fibonacci polynomials in combination with Störmer's method for the solution of Klein/Sinh-Gordon equations is proposed. Initially, the problem is transformed to a time-discrete form by using Störmer'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. |
| format | Article |
| id | doaj-art-9ad777cfbd4246fbb2a7c1b4a460f899 |
| institution | Kabale University |
| issn | 2767-8946 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj-art-9ad777cfbd4246fbb2a7c1b4a460f8992025-01-24T01:02:09ZengAIMS PressMathematical Modelling and Control2767-89462024-09-014336137310.3934/mmc.2024029Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical studyIhteram Ali0Imtiaz Ahmad1Department of Mathematics, Women University Swabi, Swabi 23430, PakistanInstitute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Kajang 43000, Selangor, MalaysiaIn this article, a hybrid numerical scheme based on Lucas and Fibonacci polynomials in combination with Störmer's method for the solution of Klein/Sinh-Gordon equations is proposed. Initially, the problem is transformed to a time-discrete form by using Störmer'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.https://www.aimspress.com/article/doi/10.3934/mmc.2024029klein/sinh-gordon equationfinite differenceslucas polynomialsfibonacci polynomials |
| spellingShingle | Ihteram Ali Imtiaz Ahmad Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study Mathematical Modelling and Control klein/sinh-gordon equation finite differences lucas polynomials fibonacci polynomials |
| 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 |
| topic | klein/sinh-gordon equation finite differences lucas polynomials fibonacci polynomials |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2024029 |
| work_keys_str_mv | AT ihteramali applicationsofthenonlinearkleinsinhgordonequationsinmodernphysicsanumericalstudy AT imtiazahmad applicationsofthenonlinearkleinsinhgordonequationsinmodernphysicsanumericalstudy |