Due to the importance of the generalized nonlinear Klein-Gordon equation (NL-KGE) in describing the behavior of light waves and nonlinear optical materials, including phenomena such as optical switching by manipulating the dispersion and nonlinearity of optical fibers and stable solitons, we explain the approximation of this model by evaluating different classical and fractional terms in this paper. To estimate the fundamental function, we use a first-order finite difference approach in the temporal direction and a collocation method based on Gegenbauer polynomials (GP) in the spatial direction to solve the NL-KGE model. Moreover, the stability and convergence analysis is proved by examining the order of the new method in the time direction as $\mathcal{O}( \delta t )$. To demonstrate the efficiency of this design, we presented numerical examples and made comparisons with other methods in the literature.
Mesgarani, H., Esmaeelzade Aghdam, Y., & Darabi, E. (2024). A new numerical method for discretization of the nonlinear Klein-Gordon model arising in light waves. Journal of Mathematical Modeling, 12(1), 71-84. doi: 10.22124/jmm.2023.25115.2230
MLA
Hamid Mesgarani; Yones Esmaeelzade Aghdam; Ezzatollah Darabi. "A new numerical method for discretization of the nonlinear Klein-Gordon model arising in light waves". Journal of Mathematical Modeling, 12, 1, 2024, 71-84. doi: 10.22124/jmm.2023.25115.2230
HARVARD
Mesgarani, H., Esmaeelzade Aghdam, Y., Darabi, E. (2024). 'A new numerical method for discretization of the nonlinear Klein-Gordon model arising in light waves', Journal of Mathematical Modeling, 12(1), pp. 71-84. doi: 10.22124/jmm.2023.25115.2230
VANCOUVER
Mesgarani, H., Esmaeelzade Aghdam, Y., Darabi, E. A new numerical method for discretization of the nonlinear Klein-Gordon model arising in light waves. Journal of Mathematical Modeling, 2024; 12(1): 71-84. doi: 10.22124/jmm.2023.25115.2230
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