We propose a nonlinear age-structured model of tumor cell population with proliferating and quiescent phases. We apply the discontinuous Galerkin (DG) method to study its dynamical behavior. The DG numerical approximation is used for the spatial discretization and then the strong-stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. This paper aims to establish more efficient results in the sense of computational approach and compare these with analogous estimates for Weighted Essentially and Non-Oscillatory (WENO) scheme. Finally, some test examples and numerical simulations are given to illustrate theoretical results and to examine the behavior of the solution.

中文翻译：

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具有增殖期和静止期的非线性年龄结构肿瘤细胞群模型的不连续 Galerkin 方法

我们提出了具有增殖期和静止期的肿瘤细胞群的非线性年龄结构模型。我们应用不连续 Galerkin (DG) 方法来研究其动力学行为。空间离散采用DG数值逼近，时间离散采用强稳保显式龙格-库塔（SSPERK）方法。本文旨在在计算方法的意义上建立更有效的结果，并将这些结果与加权本质和非振荡 (WENO) 方案的类似估计值进行比较。最后，给出了一些测试示例和数值模拟来说明理论结果并检查解决方案的行为。