A second-order numerical method for a cell population model with asymmetric division

Population balance models represent an accurate and general way of describing the complicated dynamics of cell growth. In this paper we study the numerical integration of a model for the evolution of a size-structured cell population with asymmetric division. We present and analyze a novel and efficient second-order numerical method based on the integration along the characteristic curves. We prove the optimal rate of convergence of the scheme and we ratify it by numerical simulation. Finally, we show that the numerical scheme serves as a valuable tool in order to approximate the stable size distribution of the model.