Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

A finite difference approximation for a nonlinear size-structured phytoplankton aggregation model


Authors: Azmy S. Ackleh and Robert R. Ferdinand
Journal: Quart. Appl. Math. 57 (1999), 501-520
MSC: Primary 92D25; Secondary 65M06, 92C37
DOI: https://doi.org/10.1090/qam/1704439
MathSciNet review: MR1704439
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a nonlinear model that describes the dynamics of a phytoplankton population with aggregation and competition between individual cells. A finite difference method is developed for approximating the solution of this partial differential equation. The convergence of this approximation to a unique bounded variation solution of the model is proved. Numerical results showing the accuracy of this scheme are presented.


References [Enhancements On Off] (What's this?)

  • [1] A. S. Ackleh, Parameter Estimation in a Structured Algal Coagulation Fragmentation Model, Nonlinear Analysis, Theory Methods and Applications 28, 837-854 (1997) MR 1422189
  • [2] A. S. Ackleh and B. G. Fitzpatrick, Modeling Aggregation and Growth Processes in an Algal Population Model: Analysis and Computation, Journal of Mathematical Biology 35, 480-502 (1997) MR 1478594
  • [3] A. S. Ackleh, B. G. Fitzpatrick, and T. G. Hallam, Approximation and Parameter Estimation Problems for Algal Aggregation Models, Mathematical Models and Methods in Applied Sciences 4, 291-311 (1994) MR 1282237
  • [4] A. S. Ackleh, T. G. Hallam, and Helene C. Muller Landau, Estimation of Sticking and Contact Efficiencies in Aggregation of Phytoplankton: The 1993 SIGMA Tank Experiment, Deep-Sea Research II, 42, 185-201 (1995)
  • [5] A. S. Ackleh, T. G. Hallam, and W. O. Smith, Influences of Aggregation and Grazing on Phytoplankton Dynamics and Fluxes: An Individual Based Modeling Approach, Nonlinear World 1, 473-492 (1994)
  • [6] A. S. Ackleh and K. Ito, An Implicit Finite Difference Scheme for the Nonlinear Sized-Structured Population Model, Numerical Functional Analysis and Optimization 18, 865-884 (1997) MR 1485984
  • [7] M. G. Crandall and Andrew Majda, Monotone Difference Approximations for Scalar Conservation Laws, J. Math. Comp. 34, 1-21 (1980) MR 551288
  • [8] G. A. Jackson, Compared Observed Changes in Particle Size Spectra with Those Predicted Using Coagulation Theory, Deep-Sea Research II, 42, 159-184 (1994)
  • [9] G. Jackson, A Model of Formation of Marine Algal Flocs by Physical Coagulation Processes, Deep-Sea Research 37, 1197-1211 (1990)
  • [10] I. N. McCave, Size-Spectra and Aggregation of Suspended Particles in the Deep Ocean, Deep-Sea Research 31, 329-352 (1984)
  • [11] C. R. O'Melia and K. S. Bowman, Origins and Effects of Coagulation in Lakes, Schweiz. Z. Hydrol. 46, 64-85 (1984)
  • [12] T. R. Parsons and M. Takahashi, Biological Oceanographic Processes, Pergamon Press, 1984
  • [13] U. Riebesell and D. A. Wolf-Gladrow, The Relationship between Physical Aggregation of Phytoplankton and Particle Flux: A Numerical Model, Deep-Sea Research 39, 1085-1102 (1992)
  • [14] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1994 MR 1301779
  • [15] U. Weilenmann, C. R. O'Melia, and W. Stumm, Particle Transport in Lakes: Models and Measurements, Limnology and Oceanography 34, 1-18 (1989)
  • [16] D. M. Young, Iterative Solutions of Large Linear Systems, Academic Press, New York and London, 1971 MR 0305568

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Additional Information

DOI: https://doi.org/10.1090/qam/1704439
Article copyright: © Copyright 1999 American Mathematical Society

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