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A new numerical method for discretization of the nonlinear Klein-Gordon model arising in light waves | ||
| Journal of Mathematical Modeling | ||
| دوره 12، شماره 1، خرداد 2024، صفحه 71-84 اصل مقاله (715.2 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2023.25115.2230 | ||
| نویسندگان | ||
| Hamid Mesgarani؛ Yones Esmaeelzade Aghdam* ؛ Ezzatollah Darabi | ||
| Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785 -136, I. R. Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Nonlinear Klein-Gordon equation؛ Fractional calculus؛ Collocation method؛ Gegenbauer polynomial؛ Stability | ||
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آمار تعداد مشاهده مقاله: 54 تعداد دریافت فایل اصل مقاله: 98 |
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