Numerical Analysis of a Size-Structured Population Model with a Dynamical Resource

Abstract

In this paper, we analyze the convergence of a second-order numerical method for the approximation of a size-structured population model whose dependency on the environment is managed by the evolution of a vital resource. Optimal convergence rate is derived. Numerical experiments are also reported to demonstrate the predicted accuracy of the scheme. Also, it is applied to solve a problem that describes the dynamics of a Daphnia magna population, paying attention to the unstable case.