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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  1. L. M. Abia, O. Angulo, J. C. López-Marcos. Age-structured population dynamics models and their numerical solutions. Ecol. Model., 188 (2005), 112–136.  Zbl1052.92045
  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.  Zbl1052.92045
  3. L.M. Abia, O. Angulo, J.C. López-Marcos M.A. López-Marcos.Numerical schemes for a size-structured cell population model with equal fission. Mat. Computer Model., 50 (2009), 653–664. Zbl1185.35294
  4. M. Adimy, O. Angulo, F. Crauste J.C. López-Marcos.Numerical integration of a mathematical model of hematopoietic stem cell dynamics. Computers and Math. Applic., 56 (2008), 594–606. Zbl1155.92308
  5. O. Angulo J. C. López-Marcos.Numerical integration of fully nonlinear size-structured models. Appl. Numer. Math., 50 (2004), 291–327. Zbl1071.92033
  6. M.A. Bees, O. Angulo, J.C. López-Marcos, D. Schley. Dynamics of a structured slug population model in the absence of seasonal variation. Math. Mod. Meth. in Appl. Sci., 16 (2006), 1961–1985.  Zbl1108.92039
  7. J.M. Cushing. An Introduction to Structured Populations Dynamics. CMB-NSF Regional Conference Series in Applied Mathematics. SIAM, 1998.  Zbl0939.92026
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  9. M. Iannelli, T. Kostova, F.A. Milner. A fourth-order method for numerical integration of age- and size-structured population models. Numer. Methods Partial Differential Equations, 25 (2009) 918–930.  Zbl1172.92026
  10. S.A.L.M Kooijman, J.A.J. Metz. On the dynamics of chemically stressed populations: the deduction of a population consequences from effects on individuals. Ecotox. Environ. Saf., 8 (1984), 254–274.  
  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.  Zbl0614.92014
  12. B. Perthame. Transport Equations in Biology. Birkhäuser Verlag, Basel, 2007.  Zbl1185.92006
  13. A.M. de Roos.Numerical methods for structured population models: The escalator boxcar train. Numer. Methods Partial Differential Equations, 4 (1988), 173–195. Zbl0658.92016
  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. Zbl1130.65091
  15. G.F. Webb. Theory of Nonlinear Age-Dependent Population Dynamics. Marcel Dekker, eds, New York, 1985. Zbl0555.92014

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