A numerical method for nonlinear age-structured population models with finite maximum age

O. Angulo; J. C. López-Marcos; M. A. López-Marcos; Fabio Milner

doi:10.1016/j.jmaa.2009.09.001

A numerical method for nonlinear age-structured population models with finite maximum age

O. Angulo, J. C. López-Marcos, M. A. López-Marcos, Fabio Milner

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

We propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin-MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.

Original language	English (US)
Pages (from-to)	150-160
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	361
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2009.09.001
State	Published - Jan 1 2010

Keywords

Finite maximum age
Nonlinear age-structured population model
Numerical methods

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2009.09.001

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title = "A numerical method for nonlinear age-structured population models with finite maximum age",

abstract = "We propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin-MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.",

keywords = "Finite maximum age, Nonlinear age-structured population model, Numerical methods",

author = "O. Angulo and L{\'o}pez-Marcos, {J. C.} and L{\'o}pez-Marcos, {M. A.} and Fabio Milner",

note = "Funding Information: F.A. Milner was supported in part by the NSF grant DMS-0314575. O. Angulo, J.C. L{\'o}pez-Marcos and M.A. L{\'o}pez-Marcos were supported in part by the project of the Ministerio de Educaci{\'o}n y Ciencia MTM2008-06462-C02-02, FEDER, by the project of the Junta de Castilla y Le{\'o}n VA046A07 and by the 2009 Grant Program for Excellence Research Group (GR137) of the Junta de Castilla y Le{\'o}n. M.A. L{\'o}pez-Marcos was also supported in part by the project of the Junta de Castilla y Le{\'o}n VA027A08.",

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doi = "10.1016/j.jmaa.2009.09.001",

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AU - Angulo, O.

AU - López-Marcos, J. C.

AU - López-Marcos, M. A.

AU - Milner, Fabio

N1 - Funding Information: F.A. Milner was supported in part by the NSF grant DMS-0314575. O. Angulo, J.C. López-Marcos and M.A. López-Marcos were supported in part by the project of the Ministerio de Educación y Ciencia MTM2008-06462-C02-02, FEDER, by the project of the Junta de Castilla y León VA046A07 and by the 2009 Grant Program for Excellence Research Group (GR137) of the Junta de Castilla y León. M.A. López-Marcos was also supported in part by the project of the Junta de Castilla y León VA027A08.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - We propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin-MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.

AB - We propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin-MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.

KW - Finite maximum age

KW - Nonlinear age-structured population model

KW - Numerical methods

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A numerical method for nonlinear age-structured population models with finite maximum age

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Keywords

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