A fourth-order method for numerical integration of age- and size-structured population models

Mimmo Lannelli, Tanya Kostova, Fabio Augusto Milner

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

In many applications of age- and size-structured population models, there is an interest in obtaining good approximations of total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. In this article, we present a general framework and a specific example of a fourth-order method based on composite Newton-Cotes quadratures for a size-structured population model.

Original languageEnglish (US)
Pages (from-to)918-930
Number of pages13
JournalNumerical Methods for Partial Differential Equations
Volume25
Issue number4
DOIs
StatePublished - Jul 2009

Keywords

  • Finite differences
  • Quadratures
  • Size-structured equations

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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