We study a mathematical model of cancer cell invasion of tissue (extracellular matrix) consisting of a system of reaction–diffusion-taxis partial differential equations which describes the interactions between cancer cells, the matrix degrading enzyme and the host tissue. We analyze the local stability of the constant equilibrium solutions to the chemotaxis–haptotaxis system, we derive a discretization of the system by means of the Generalized Finite Difference Method (GFDM) and we prove the convergence of the discrete solution to the analytical one. Also, we provide several numerical examples on the applications of this meshless method over regular and irregular domains.

我们研究了癌细胞入侵组织（细胞外基质）的数学模型，该模型由反应-扩散-出租车偏微分方程组组成，该系统描述了癌细胞，基质降解酶和宿主组织之间的相互作用。我们分析了趋化趋向轴系统的恒定平衡解的局部稳定性，通过广义有限差分法（GFDM）导出了系统的离散化，并证明了离散解与解析解的收敛性。此外，我们提供了一些有关此无网格方法在规则和不规则域上的应用的数值示例。