Abstract
In this paper we develop a high order explicit finite difference weighted essentially non-oscillatory (WENO) scheme for solving a hierarchical size-structured population model with nonlinear growth, mortality and reproduction rates. The main technical complication is the existence of global terms in the coefficient and boundary condition for this model. We carefully design approximations to these global terms and boundary conditions to ensure high order accuracy. Comparing with the first order monotone and second order total variation bounded schemes for the same model, the high order WENO scheme is more efficient and can produce accurate results with far fewer grid points. Numerical examples including one in computational biology for the evolution of the population of Gambussia affinis, are presented to illustrate the good performance of the high order WENO scheme.
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Chi-Wang Shu was supported in part by NSFC grant 10671190 while he was visiting the Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China. Additional support was provided by ARO grant W911NF-04-1-0291 and NSF grant DMS-0510345.
Mengping Zhang was supported in part by NSFC grant 10671190.
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Shen, J., Shu, CW. & Zhang, M. A High Order WENO Scheme for a Hierarchical Size-Structured Population Model. J Sci Comput 33, 279–291 (2007). https://doi.org/10.1007/s10915-007-9152-x
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DOI: https://doi.org/10.1007/s10915-007-9152-x