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Complex Ginzburg–Landau equation with generalized finite differences

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Salete, Eduardo and Vargas, A. M. and García, Ángel and Negreanu, Mihaela and Benito, Juan J. and Ureña, Francisco (2020) Complex Ginzburg–Landau equation with generalized finite differences. Mathematics, 8 (12). p. 2248. ISSN 2227-7390

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Official URL: https://doi.org/10.3390/math8122248




Abstract

In this paper we obtain a novel implementation for irregular clouds of nodes of the meshless method called Generalized Finite Difference Method for solving the complex Ginzburg–Landau equation. We derive the explicit formulae for the spatial derivative and an explicit scheme by splitting the equation into a system of two parabolic PDEs. We prove the conditional convergence of the numerical scheme towards the continuous solution under certain assumptions. We obtain a second order approximation as it is clear from the numerical results. Finally, we provide several examples of its application over irregular domains in order to test the accuracy of the explicit scheme, as well as comparison with other numerical methods.


Item Type:Article
Uncontrolled Keywords:Ginzburg–Landau equation; parabolic-parabolic systems; generalized finite difference method
Palabras clave (otros idiomas):Ecuación de Ginzburg-Landau
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:63706
Deposited On:21 Jan 2021 12:28
Last Modified:25 Jan 2021 08:46

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