Long-Time Simulation of a Size-Structured Population Model with a Dynamical Resource

L. M. Abia; O. Angulo; J. C. López-Marcos; M. A. López-Marcos

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 6, page 1-21
  • ISSN: 0973-5348

Abstract

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In this paper, we study the numerical approximation of a size-structured population model whose dependency on the environment is managed by the evolution of a vital resource. We show that this is a difficult task: some numerical methods are not suitable for a long-time integration. We analyze the reasons for the failure.

How to cite

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Abia, L. M., et al. "Long-Time Simulation of a Size-Structured Population Model with a Dynamical Resource." Mathematical Modelling of Natural Phenomena 5.6 (2010): 1-21. <http://eudml.org/doc/197682>.

@article{Abia2010,
abstract = {In this paper, we study the numerical approximation of a size-structured population model whose dependency on the environment is managed by the evolution of a vital resource. We show that this is a difficult task: some numerical methods are not suitable for a long-time integration. We analyze the reasons for the failure.},
author = {Abia, L. M., Angulo, O., López-Marcos, J. C., López-Marcos, M. A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {size-structured population model; dynamical resource; numerical methods},
language = {eng},
month = {4},
number = {6},
pages = {1-21},
publisher = {EDP Sciences},
title = {Long-Time Simulation of a Size-Structured Population Model with a Dynamical Resource},
url = {http://eudml.org/doc/197682},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Abia, L. M.
AU - Angulo, O.
AU - López-Marcos, J. C.
AU - López-Marcos, M. A.
TI - Long-Time Simulation of a Size-Structured Population Model with a Dynamical Resource
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/4//
PB - EDP Sciences
VL - 5
IS - 6
SP - 1
EP - 21
AB - In this paper, we study the numerical approximation of a size-structured population model whose dependency on the environment is managed by the evolution of a vital resource. We show that this is a difficult task: some numerical methods are not suitable for a long-time integration. We analyze the reasons for the failure.
LA - eng
KW - size-structured population model; dynamical resource; numerical methods
UR - http://eudml.org/doc/197682
ER -

References

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  2. L. M. Abia, O. Angulo, J. C. López-Marcos. Size-structured population dynamics models and their numerical solutions. Discrete Contin. Dyn. Syst. B, 4 (2004), 1203–1222.  
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  11. J.A.J. Metz and E.O. Dieckmann, editors. The Dynamics of Physiologically Structured Populations. Springer Lecture Notes in Biomathematics, 68. Springer, Heildelberg, 1986.  
  12. B. Perthame. Transport Equations in Biology. Birkhäuser Verlag, Basel, 2007.  
  13. A.M. de Roos.Numerical methods for structured population models: The escalator boxcar train. Numer. Methods Partial Differential Equations, 4 (1988), 173–195. 
  14. J. Shen, C.W. Shu M.P. Zhang. A high order WENO scheme for a hierarchical size-structured population model. J. Sci. Comput., 33 (2007), 279–291. 
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