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A numerical method for a nonlinear structured population model with an indefinite growth rate coupled with the environment. (English) Zbl 1431.65129

Summary: 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.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
34B60 Applications of boundary value problems involving ordinary differential equations
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