Analysis of a semi-Lagrangian numerical method in a cell dwarfism model

In this work, we introduce a new semi-Lagrangian numerical method proposed to solve a cell population balance model which describes cell dwarfism, by allowing cell division at any size. We analyse its convergence and derive an optimal rate. Numerical experiments are reported to demonstrate the predi...

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Bibliographic Details
Published in:International journal of computer mathematics 2022-12, Vol.ahead-of-print (ahead-of-print), p.1-13
Main Authors: Abia, L. M., Angulo, O., López-Marcos, J. C., López-Marcos, M. A.
Format: Article
Language:English
Subjects:
Cell population balance model
convergence analysis
dwarfism
semi-Lagrangian method
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Summary:In this work, we introduce a new semi-Lagrangian numerical method proposed to solve a cell population balance model which describes cell dwarfism, by allowing cell division at any size. We analyse its convergence and derive an optimal rate. Numerical experiments are reported to demonstrate the predicted accuracy of the scheme. Finally, the good behaviour of the numerical method is exhibited in stressed conditions that can provoke lack of smoothness and simulations are included to show how the increase in the division rate of small size-cells promotes dynamics in which nonfunctional dwarf cells are saturating the total cell population.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2022.2159394