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Analysis and numerics for an age‐ and sex‐structured population model
Author(s) -
Pokojovy Michael,
Skvarkovskyi Yevhenii
Publication year - 2016
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.22032
Subject(s) - mathematics , hilbert space , semigroup , partial differential equation , convergence (economics) , stability (learning theory) , population , population model , space (punctuation) , mathematical analysis , computer science , demography , economic growth , operating system , machine learning , sociology , economics
We study a linear model of McKendrick‐von Foerster‐Keyfitz type for the temporal development of the age structure of a two‐sex human population. For the underlying system of partial integro‐differential equations, we exploit the semigroup theory to show the classical well‐posedness and asymptotic stability in a Hilbert space framework under appropriate conditions on the age‐specific mortality and fertility moduli. Finally, we propose an implicit finite difference scheme to numerically solve this problem and prove its convergence under minimal regularity assumptions. A real data application is also given. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 706–736, 2016