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High Resolution Schemes for a Hierarchical Size-Structured Model

Jun Shen, Chi-Wang Shu and Mengping Zhang
SIAM Journal on Numerical Analysis
Vol. 45, No. 1 (2007), pp. 352-370
Stable URL: http://www.jstor.org/stable/40232932
Page Count: 19
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High Resolution Schemes for a Hierarchical Size-Structured Model
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Abstract

In this paper we discuss two explicit finite difference schemes, namely a first order upwind scheme and a second order high resolution scheme, for solving a hierarchical size-structured population model with nonlinear growth, mortality, and reproduction rates. We prove stability and convergence for both schemes and provide numerical examples to demonstrate their capability in solving smooth and discontinuous solutions.

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