@article{Ali2024, 
author = {Ihteram Ali and Imtiaz Ahmad},
title = {Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study},
year = {2024},
journal = {Mathematical Modelling and Control},
volume = {4},
number = {3},
pages = {361-373},
keywords = {Klein/Sinh-Gordon equation, finite differences, Lucas polynomials, Fibonacci polynomials},
url = {https://www.sciopen.com/article/10.3934/mmc.2024029},
doi = {10.3934/mmc.2024029},
abstract = {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.}
}