Convergence and Numerical Solution of a Model for Tumor Growth

Juan J. Benito, Ángel García, María Lucía Gavete, Mihaela Negreanu, Francisco Ureña and Antonio M. Vargas
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Juan J. Benito: ETSII, UNED, 28040 Madrid, Spain
Ángel García: ETSII, UNED, 28040 Madrid, Spain
María Lucía Gavete: Consejería Educación de Madrid, 28014 Madrid, Spain
Mihaela Negreanu: Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, UCM, 28040 Madrid, Spain
Francisco Ureña: ETSII, UNED, 28040 Madrid, Spain
Antonio M. Vargas: Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, UCM, 28040 Madrid, Spain

Mathematics, 2021, vol. 9, issue 12, 1-15

Abstract: In this paper, we show the application of the meshless numerical method called “Generalized Finite Diference Method” (GFDM) for solving a model for tumor growth with nutrient density, extracellular matrix and matrix degrading enzymes, [recently proposed by Li and Hu]. We derive the discretization of the parabolic–hyperbolic–parabolic–elliptic system by means of the explicit formulae of the GFDM. We provide a theoretical proof of the convergence of the spatial–temporal scheme to the continuous solution and we show several examples over regular and irregular distribution of points. This shows the feasibility of the method for solving this nonlinear model appearing in Biology and Medicine in complicated and realistic domains.

Keywords: generalized finite difference method; meshless numerical method; numerical convergence; tumor growth; parabolic-hyperbolic system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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