Complex Ginzburg–Landau Equation with Generalized Finite Differences

Eduardo Salete, Antonio M. Vargas, Ángel García, Mihaela Negreanu, Juan J. Benito and Francisco Ureña
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Eduardo Salete: ETSII, UNED, 28080 Madrid, Spain
Antonio M. Vargas: Departamento de Análisis Matemático y Matemática Aplicada, UCM, 28080 Madrid, Spain
Ángel García: ETSII, UNED, 28080 Madrid, Spain
Mihaela Negreanu: Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, UCM, 28080 Madrid, Spain
Juan J. Benito: ETSII, UNED, 28080 Madrid, Spain
Francisco Ureña: ETSII, UNED, 28080 Madrid, Spain

Mathematics, 2020, vol. 8, issue 12, 1-13

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.

Keywords: Ginzburg–Landau equation; parabolic-parabolic systems; generalized finite difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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