In this paper, we go through the development of a new numerical method to obtain the
solution to a size-structured population model that describes the evolution of a consumer feeding on a
dynamical resource that reacts to the environment with a lag-time response. The problem involves the
coupling of the partial differential equation that represents the population evolution and an ordinary
differential equation with a constant delay that describes the evolution of the resource. The numerical
treatment of this problem has not been considered before when a delay is included in the resource
evolution rate. We analyzed the numerical scheme and proved a second-order rate of convergence by
assuming enough regularity of the solution. We numerically confirmed the theoretical results with an
academic test problem.
