Convergence and Numerical Solution of a Model for Tumor Growth
| Autor: | F. Ureña, A. García, A.M. Vargas, Juan José Benito, Mihaela Negreanu, María Lucía Gavete |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Discretization
Explicit formulae General Mathematics 01 natural sciences 03 medical and health sciences Matrix (mathematics) 0302 clinical medicine Convergence (routing) QA1-939 generalized finite difference method Computer Science (miscellaneous) Applied mathematics Tumor growth 0101 mathematics numerical convergence Engineering (miscellaneous) Mathematics meshless numerical method Continuous solution Numerical analysis parabolic-hyperbolic system 010101 applied mathematics tumor growth Distribution (mathematics) 030220 oncology & carcinogenesis Análisis matemático |
| Zdroj: | Mathematics Volume 9 Issue 12 Mathematics, Vol 9, Iss 1355, p 1355 (2021) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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