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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| Summary: | 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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