A numerical study on the estimation of the stable size distribution for a cell population balance model

Abstract

The presence of a steady‐state distribution is an important issue in the modelization of cell populations. In this paper, we analyse, from a numerical point of view, the approach to the stable size distribution for a size‐structured balance model with an asymmetric division rate. To this end, we introduce a second‐order numerical method on the basis of the integration along the characteristic curves over the natural grid. We validate the interest of the scheme by means of a detailed analysis of convergence.

Numerical analysis of a cell dwarfism model

“…In the case of general structured population models, many numerical methods have been proposed to solve them (see [1,13] and references therein). With respect to the study of CPBMs, different techniques have been used for both symmetric and asymmetric division rates (see [2,4,5,3] and the references therein). However, all of them are proposed for the solution of models with a minimal cell division size, and it is very important to design numerical schemes specially adapted to the features of this particular CPBM.…”