结构种群模型的分裂粒子方法：收敛性及应用
Splitting-Particle Methods for Structured Population Models: Convergence and Applications
摘要：
基于算子分裂和粒子近似的思想，我们提出了一种新的数值格式，适用于一类结构化种群模型。该方案与生物学中常用的Escalator Boxcar训练（EBT）方法有关，EBT方法本质上类似于物理学中使用的粒子方法。我们的方法利用分裂的技术，由于在方程中的传输步骤和非局部积分项可以单独考虑。在有限个非负Radon测度的自然空间中，得到了该方法的收敛阶。这种收敛性的研究，即使在粒子模拟中添加重建和近似步骤，以保持控制下的近似粒子的数量。我们验证了我们的计划在几个测试情况下，理论上的收敛误差。最后，我们使用该计划的情况下，EBT方法不适用于显示这种新方法的灵活性，以应付一般结构化人口模型中的不同条款。
英文摘要：
We propose a new numerical scheme designed for a wide class of structured population models based on the idea of operator splitting and particle approximations. This scheme is related to the Escalator Boxcar Train (EBT) method commonly used in biology, which is in essence an analogue of particle methods used in physics. Our method exploits the split-up technique, thanks to which the transport step and the nonlocal integral terms in the equation can be separately considered. The order of convergence of the proposed method is obtained in the natural space of finite nonnegative Radon measures equipped with the flat metric. This convergence is studied even adding reconstruction and approximation steps in the particle simulation to keep the number of approximation particles under control. We validate our scheme in several test cases showing the theoretical convergence error. Finally, we use the scheme in situations in which the EBT method does not apply showing the flexibility of this new method to cope with the different terms in general structured population models.
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