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Convergence and Numerical Solution of a Model for Tumor Growth

Author

Listed:
  • Juan J. Benito

    (ETSII, UNED, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Ángel García

    (ETSII, UNED, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • María Lucía Gavete

    (Consejería Educación de Madrid, 28014 Madrid, Spain
    These authors contributed equally to this work.)

  • Mihaela Negreanu

    (Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, UCM, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Francisco Ureña

    (ETSII, UNED, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Antonio M. Vargas

    (Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, UCM, 28040 Madrid, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Juan J. Benito & Ángel García & María Lucía Gavete & Mihaela Negreanu & Francisco Ureña & Antonio M. Vargas, 2021. "Convergence and Numerical Solution of a Model for Tumor Growth," Mathematics, MDPI, vol. 9(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1355-:d:573313
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    Cited by:

    1. Francisco Ureña & Ángel García & Antonio M. Vargas, 2022. "Preface to “Applications of Partial Differential Equations in Engineering”," Mathematics, MDPI, vol. 11(1), pages 1-4, December.

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