Premium
A fourth‐order method for numerical integration of age‐ and size‐structured population models
Author(s) -
Iannelli Mimmo,
Kostova Tanya,
Milner Fabio Augusto
Publication year - 2009
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20381
Subject(s) - mathematics , quadrature (astronomy) , numerical integration , convergence (economics) , partial derivative , population , numerical analysis , partial differential equation , nyström method , order (exchange) , mathematical analysis , calculus (dental) , integral equation , medicine , demography , engineering , finance , dentistry , sociology , electrical engineering , economics , economic growth
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. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009