Prostate cancer (PCa) is a significant global health concern that affects the male population. In this study, we present a numerical approach to simulate the growth of PCa tumors and their response to drug therapy. The approach is based on a previously developed model, which consists of a coupled system comprising one phase field equation and two reaction–diffusion equations. To solve this system, we employ the fast second-order exponential time differencing Runge–Kutta (ETDRK2) method with stabilizing terms. This method is a decoupled linear numerical algorithm that preserves three crucial physical properties of the model: a maximum bound principle (MBP) on the order parameter and non-negativity of the two concentration variables. Our simulations allow us to predict tumor growth patterns and outcomes of drug therapy over extended periods, offering valuable insights for both basic research and clinical treatments.

中文翻译：

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前列腺癌治疗生长相场模型的最大束缚原理和非负保留 ETD 方案

前列腺癌 (PCa) 是影响男性人口的一个重大全球健康问题。在这项研究中，我们提出了一种数值方法来模拟 PCa 肿瘤的生长及其对药物治疗的反应。该方法基于先前开发的模型，该模型由一个耦合系统组成，该耦合系统包含一个相场方程和两个反应扩散方程。为了求解该系统，我们采用具有稳定项的快速二阶指数时间差分龙格-库塔 (ETDRK2) 方法。该方法是一种解耦线性数值算法，保留了模型的三个关键物理特性：阶数参数的最大界限原理 (MBP) 和两个浓度变量的非负性。我们的模拟使我们能够预测长期的肿瘤生长模式和药物治疗的结果，为基础研究和临床治疗提供有价值的见解。