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

Producción CientíficaPopulation 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 andweratify it by numerical simulation. Finally,weshow that the numerical scheme serves as a valuable tool in order to approximate the stable size distribution of the model.Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA191U13

A Second-Order Method for the Numerical Integration of a Size-Structured Cell Population Model

Producción CientíficaWe consider the numerical integration of a size-structured cell population model. We propose a new second-order numerical method to attain its solution. The scheme is analyzed and the optimal rate of convergence is derived. We show experimentally the predicted accuracy of the scheme.Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA191U13

Study on the efficiency in the numerical integration of size-structured population models: Error and computational cost

Producción CientíficaWe describe a procedure which is useful to select an appropriate numerical method in a size-structured population model. We consider four different numerical methods based on finite difference schemes or characteristics curves integration. We compute an analytical approximation in terms of the discretization parameters for the theoretical error principal terms and the computational cost. Thus, we show the efficiency curve that allows to select the best relationship between the discretization parameters for each numerical method. Finally, we obtain the most efficient numerical method for each test.Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA191U13

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

Producción CientíficaIn 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.Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA191U13

Analysis of an efficient integrator for a size-structured population model with a dynamical resource

Producción CientíficaIn this paper, an efficient numerical method for the approximation of a nonlinear size-structured population model is presented. The nonlinearity of the model is given by dependency on the environment through the consumption of a dynamical resource. We analyse the properties of the numerical scheme and optimal second-order convergence is derived. We report experiments with academical tests to demonstrate numerically the predicted accuracy of the scheme. The model is applied to solve a biological problem: the dynamics of an ectothermic population (the water flea, Daphnia magna). We analyse its long time evolution and describe the asymptotically stable steady states, both equilibria and limit cycles.Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA191U13

Numerical integration of a hierarchically size-structured population model with contest competition

Producción CientíficaWe formulate schemes for the numerical solution to a hierarchically size-structured population model. The schemes are analysed and optimal rates of convergence are derived. Some numerical experiments are also reported to demonstrate the predicted accuracy of the schemes and to show their behaviour to approaching stable steady states.Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA191U13

Numerical analysis of a cell dwarfism model

Producción CientíficaIn this work, we study numerically a model which describes cell dwarfism. It consists in a pure initial value problem for a first order partial differential equation, that can be applied to the description of the evolution of diseases as thalassemia. We design two numerical methods that prevent the use of the characteristic curve x = 0, and derive their optimal rates of convergence. Numerical experiments are also reported in order to demonstrate the predicted accuracy of the schemes. Finally, a comparison study on their efficiency is presented.Junta de Castilla y León and European FEDER Funds (VA041P17)Junta de Castilla y León (VA138G18)Ministerio de Economía, Industria y Competitividad and European FEDER Funds (Project MTM2014-56022-C2-2-P)Ministerio de Ciencia e Innovación (Proyect MTM2017-85476-C2-P

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

Producción CientíficaThe presence of a steady-state distribution is an important issue in the modelization of cell populations. In this paper,we analyse, froma 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.Ministerio de Economía, Industria y Competitividad and European FEDER (Project MTM2014‐56022‐C2‐2‐P)Ministerio de Economía, Industria y Competitividad (Project MTM2017‐85476‐C2‐1‐P)Junta de Castilla y León and European FEDER Funds (Project VA041P17