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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:309

Article; Proceedings Paper

Angulo, O.^1,2  Lopez-Marcos, J. C.^3,4  Lopez-Marcos, M. A.^3,4 

[1] Univ Valladolid, Dept Matemat Aplicada, ETSIT, Pso Belen 5, E-47011 Valladolid, Spain

[2] Univ Valladolid, ETSIT, IMUVA, Pso Belen 5, E-47011 Valladolid, Spain

[3] Univ Valladolid, Fac Ciencias, Dept Matemat Aplicada, Pso Belen 7, E-47011 Valladolid, Spain

[4] Univ Valladolid, Fac Ciencias, IMUVA, Pso Belen 7, E-47011 Valladolid, Spain

关键词: Size-structured population;    Cell population models;    Asymmetric division;    Numerical methods;    Characteristics method;    Convergence analysis;   

DOI  :  10.1016/j.cam.2016.03.008

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free