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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2014-11-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.233 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1551-0018 |