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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-09-01
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| Series: | Mathematical Modelling and Control |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2024029 |
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| Summary: | 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. |
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| ISSN: | 2767-8946 |