Numerical analysis of an open marine population model with spaced-limited recruitment

Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics

“…By means of similar arguments than in Theorem 4.1, and using the convergence properties of the quadrature rules that are included in the description of the numerical scheme, we can arrive to the following result which shows that the equilibrium solution of the numerical method (6)- (9) converges to the equilibrium solution of the truncated problem as k tends to zero. More precisely, the convergence is of second order.…”

“…In [1,2], we can find a review of the numerical schemes proposed to solve models of physiologically structured populations, which are compared with regards to accuracy, efficiency, generality, mathematical methodology and qualitative behavior depending on the compatibility conditions between initial and boundary data of the problems. On the other hand, modern numerical methods have been successfully applied to physiologically structured models to replicate available field and/or laboratory A c c e p t e d M a n u s c r i p t data, for a variety of different systems [3,[7][8][9][10][11]15]. All these works indicate that structured population models and numerical simulations are valid tools to investigate systems such as the one under consideration here.…”

Numerical approximation of finite life‐span age‐structured population models

“…Some authors have used this change to simplify the model and, then, approach it numerically, for example, in order to describe the evolution of the age profile of a general population, 13 or to approximate the dynamics of a particular population 8‐10 . However, in all these cases, it is essential to know the exact values of π to produce a convergent numerical method approximating the density function.…”

“…For the numerical approximation of the finite life‐span age‐structured population models, different approaches have been proposed. Some of them require an exact knowledge of the survival function 8‐13 . Other works 14‐20 (and more specifically, for the non‐linear case with separable mortality) assume an age‐specific part with a particular expression near the maximum age.…”

A semi-Lagrangian method for a cell population model in a dynamical environment

“…It is to be expected that analytical solutions of (1.1)-(1.4) are difficult to obtain except in some simplified situations. Therefore we need approximation schemes to solve more realistic problems (numerical methods shown its efficiency in different applied models [4][5][6][7][8][9][10][11]). From a numerical point of view, the integration of cell models has been initially studied in recent years.…”