In this article we develop a second-order high resolution finite difference method for a general size-structured population model coupled with environmental dynamics where the individual growth rate may change sign. The model consists of a first order hyperbolic partial differential equation describing the population density of individuals coupled with a system of ordinary differential equations describing the environment. This model notably features nonlocal nonlinearities in the vital rates of individuals which are allowed to depend on the environmental dynamics. We develop rigorous estimates to establish stability of the high-resolution finite-difference numerical scheme, as well as its convergence to the unique weak solution of the nonlinear model. Numerical experiments are provided to demonstrate the order of convergence of the scheme and to compare its performance against first-order finite difference methods. The scheme is then applied to a biologically relevant example developed to investigate the steady state dynamics of a population where the vital rates of individuals exhibit size specific effects and nonlocal dependence on environmental resource levels. In particular, the example investigates the role of newborn growth rates, nonlocal weight factors, resource thresholds, and minimum reproductive size on steady state population distributions and limits on the maximum size of individuals.

在本文中，我们为一般规模结构的种群模型开发了一种二阶高分辨率有限差分方法，该模型与环境动态相结合，其中个体增长率可能会改变符号。该模型由描述个体人口密度的一阶双曲偏微分方程和描述环境的常微分方程组组成。该模型的显着特征是个体生命率的非局部非线性，这取决于环境动态。我们开发了严格的估计，以建立高分辨率有限差分数值方案的稳定性，以及它对非线性模型的唯一弱解的收敛性。提供了数值实验来证明该方案的收敛顺序，并将其性能与一阶有限差分方法进行比较。然后将该方案应用于开发的生物学相关示例，以研究人口的稳态动态，其中个体的生命率表现出大小特定的影响和对环​​境资源水平的非局部依赖性。特别是，该示例研究了新生儿增长率、非局部权重因素、资源阈值和最小繁殖规模对稳态人口分布和个体最大规模限制的作用。然后将该方案应用于开发的生物学相关示例，以研究人口的稳态动态，其中个体的生命率表现出大小特定的影响和对环​​境资源水平的非局部依赖性。特别是，该示例研究了新生儿增长率、非局部权重因素、资源阈值和最小繁殖规模对稳态人口分布和个体最大规模限制的作用。然后将该方案应用于开发的生物学相关示例，以研究人口的稳态动态，其中个体的生命率表现出大小特定的影响和对环​​境资源水平的非局部依赖性。特别是，该示例调查了新生儿增长率、非局部权重因素、资源阈值和最小繁殖规模对稳态人口分布的作用以及对个体最大规模的限制。