<p> We consider a size-structured population model where individuals may be recruited into the population at different sizes. First and second order finite difference schemes are developed to approximate the solution of the model. The convergence of the approximations to a unique weak solution is proved. We then show that as the distribution of the new recruits become concentrated at the smallest size, the weak solution of the distributed states-at-birth model converges to the weak solution of the classical Sinko-Streifer type size-structured model in the weak* topology. Numerical simulations are provided to demonstrate the achievement of the desired accuracy of the two methods for smooth solutions as well as the superior performance of the second-order method in resolving solution-discontinuities. A least-squares method is developed for estimating parameters in a size-structured population model with distributed states-at-birth from field data. The first and second order finite difference schemes for approximating solution of the model are utilized in the least-squares problem. Convergence results for the computed parameters are established. Numerical results demonstrating the efficiency of the technique are provided. </p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10163274 |
| Date | 01 December 2016 |
| Creators | Li, Xinyu |
| Publisher | University of Louisiana at Lafayette |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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