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

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Benito, J.J. and García, A. and Gavete, L. and Negreanu, Mihaela and Ureña, F. and Vargas, A. M. (2020) On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences. Engineering Analysis with Boundary Elements, 113 . pp. 181-190. ISSN 09557997

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Official URL: https://doi.org/10.1016/j.enganabound.2020.01.002




Abstract

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.


Item Type:Article
Uncontrolled Keywords:Chemotaxis models; Parabolic-elliptic systems; Generalized Finite Difference method
Palabras clave (otros idiomas):Método de las diferencias finitas generalizadas
Subjects:Sciences > Mathematics > Numerical analysis
Sciences > Mathematics > Differential equations
Sciences > Chemistry > Molecular biology
ID Code:63714
Deposited On:17 Feb 2021 15:07
Last Modified:18 Feb 2021 07:54

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