On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences

In the present paper we propose the Generalized Finite Difference Method (GFDM) for numerical solution of a cross-diffusion system with chemotactic terms. We derive the discretization of the system using a GFD scheme in order to prove and illustrate that the uniform stability behavior/ convergence o...

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Detalhes bibliográficos
Autores: Benito, J.J., García, A., Gavete, L., Negreanu Pruna, Mihaela, Ureña, F., Vargas, A. M.
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/7731
Acesso em linha:https://hdl.handle.net/20.500.14352/7731
Access Level:acceso abierto
Palavra-chave:519.6
Chemotaxis models
Parabolic-elliptic systems
Generalized Finite Difference method
Método de las diferencias finitas generalizadas
Análisis numérico
Ecuaciones diferenciales
Biología molecular (Química)
1206 Análisis Numérico
1202.07 Ecuaciones en Diferencias
Descrição
Resumo:In the present paper we propose the Generalized Finite Difference Method (GFDM) for numerical solution of a cross-diffusion system with chemotactic terms. We derive the discretization of the system using a GFD scheme in order to prove and illustrate that the uniform stability behavior/ convergence of the continuous model is also preserved for the discrete model. We prove the convergence of the explicit method and give the conditions of convergence. Extensive numerical experiments are presented to illustrate the accuracy, efficiency and robustness of the GFDM.