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A numerical method for a nonlinear structured population model with an indefinite growth rate coupled with the environment
Author(s) -
Ackleh Azmy S.,
Miller Robert L.
Publication year - 2019
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.22418
Subject(s) - mathematics , nonlinear system , ode , bounded function , population , stability (learning theory) , sign (mathematics) , domain (mathematical analysis) , population model , finite difference , numerical stability , convergence (economics) , rate of convergence , mathematical optimization , numerical analysis , mathematical analysis , computer science , channel (broadcasting) , computer network , physics , demography , quantum mechanics , machine learning , sociology , economics , economic growth
A numerical method is developed for a general structured population model coupled with the environment dynamics over a bounded domain where the individual growth rate changes sign. Sign changes notably exhibit nonlocal dependence on the population density and environmental factors (e.g., resource availability and other habitat variables). This leads to a highly nonlinear PDE describing the time‐evolution of the population density coupled with a nonlinear‐nonlocal system of ODEs describing the environmental time‐dynamics. Stability of the finite‐difference numerical scheme and its convergence to the unique weak solution are proved. Numerical experiments are provided to demonstrate the performance of the finite difference scheme and to illustrate a range of biologically relevant potential applications.