Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model
We study a quasilinear hierarchically size-structured population modelpresented in [4]. In this model the growth, mortality andreproduction rates are assumed to depend on a function of thepopulation density. In [4] we showed that solutions to thismodel can become singular (measure-valued) in finite...
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.233 |
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| author | Azmy S. Ackleh Vinodh K. Chellamuthu Kazufumi Ito |
| author_facet | Azmy S. Ackleh Vinodh K. Chellamuthu Kazufumi Ito |
| author_sort | Azmy S. Ackleh |
| collection | DOAJ |
| description | We study a quasilinear hierarchically size-structured population modelpresented in [4]. In this model the growth, mortality andreproduction rates are assumed to depend on a function of thepopulation density. In [4] we showed that solutions to thismodel can become singular (measure-valued) in finite time even ifall the individual parameters are smooth. Therefore, in this paperwe develop a first order finite difference scheme to compute thesemeasure-valued solutions. Convergence analysis for this method isprovided. We also develop a high resolution second order scheme tocompute the measure-valued solution of the model and perform a comparative study between thetwo schemes. |
| format | Article |
| id | doaj-art-56761351f3994dd5949b06e292f7967d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-56761351f3994dd5949b06e292f7967d2025-01-24T02:31:45ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-0112223325810.3934/mbe.2015.12.233Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population modelAzmy S. Ackleh0Vinodh K. Chellamuthu1Kazufumi Ito2Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205We study a quasilinear hierarchically size-structured population modelpresented in [4]. In this model the growth, mortality andreproduction rates are assumed to depend on a function of thepopulation density. In [4] we showed that solutions to thismodel can become singular (measure-valued) in finite time even ifall the individual parameters are smooth. Therefore, in this paperwe develop a first order finite difference scheme to compute thesemeasure-valued solutions. Convergence analysis for this method isprovided. We also develop a high resolution second order scheme tocompute the measure-valued solution of the model and perform a comparative study between thetwo schemes.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.233finite-difference approximationshierarchically size-structured population modelmeasure-valuedsolutionsconvergence analysis. |
| spellingShingle | Azmy S. Ackleh Vinodh K. Chellamuthu Kazufumi Ito Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model Mathematical Biosciences and Engineering finite-difference approximations hierarchically size-structured population model measure-valuedsolutions convergence analysis. |
| title | Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model |
| title_full | Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model |
| title_fullStr | Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model |
| title_full_unstemmed | Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model |
| title_short | Finite difference approximations for measure-valued solutions of a hierarchicallysize-structured population model |
| title_sort | finite difference approximations for measure valued solutions of a hierarchicallysize structured population model |
| topic | finite-difference approximations hierarchically size-structured population model measure-valuedsolutions convergence analysis. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.233 |
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