On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences. (April 2020)

• Record Type: Journal Article
• Authors: Benito, J.J.; García, A.; Gavete, L.; Negreanu, M.; Ureña, F.; Vargas, A.M.
• Is Part Of: Engineering analysis with boundary elements. Volume 113(2020)
• Page Start: 181
• Page End: 190
• Publication Date: 2020-04
• Subjects: Chemotaxis models -- Parabolic-elliptic systems -- Generalized Finite Difference method; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2020.01.002
• Languages: English
• ISSNs: 0955-7997

Abstract

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.