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.

中文翻译：

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肿瘤生长模型的收敛性和数值解

在本文中，我们展示了称为“广义有限差分法”（GFDM）的无网格数值方法在求解具有营养密度、细胞外基质和基质降解酶的肿瘤生长模型中的应用，[最近由 Li 和 Hu 提出]。我们通过 GFDM 的显式公式推导出抛物线-双曲线-抛物线-椭圆系统的离散化。我们提供了空间-时间方案收敛到连续解的理论证明，并展示了规则和不规则点分布的几个例子。这显示了解决这种非线性模型的方法在复杂和现实领域出现在生物和医学中的可行性。