Article ID Journal Published Year Pages File Type
4639849 Journal of Computational and Applied Mathematics 2011 13 Pages PDF
Abstract

In this paper we develop high order positivity-preserving finite volume weighted essentially non-oscillatory (WENO) schemes for solving a hierarchical size-structured population model with nonlinear growth, mortality and reproduction rates. We carefully treat the technical complications in boundary conditions and global integration terms to ensure high order accuracy and the positivity-preserving property. Comparing with the previous high order difference WENO scheme for this model, the positivity-preserving finite volume WENO scheme has a comparable computational cost and accuracy, with the added advantages of being positivity-preserving and having L1L1 stability. Numerical examples, including that of the evolution of the population of Gambusia affinis, are presented to illustrate the good performance of the scheme.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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