Complex Ginzburg–Landau Equation with Generalized Finite Differences

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 equatio...

Descripción completa

Detalles Bibliográficos
Autores: Salete Casino, Eduardo, Vargas Ureña, Antonio Manuel, García, Ángel, Negreanu, Mihaela, Benito Muñoz, Juan J., Ureña, Francisco
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/25119
Acceso en línea:https://hdl.handle.net/20.500.14468/25119
Access Level:acceso abierto
Palabra clave:33 Ciencias Tecnológicas::3310 Tecnología industrial
Ginzburg–Landau equation
parabolic-parabolic systems
generalized finite difference method
Descripción
Sumario: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.