A pseudospectral method for investigating the stability of linear population models with two physiological structures
| Autor: | Alessia Andò, Simone De Reggi, Davide Liessi, Francesca Scarabel |
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| Rok vydání: | 2022 |
| Předmět: |
37M99
65L07 65N25 (Primary) 35L04 37N25 47D06 92D25 (Secondary) infinitesimal generator Applied Mathematics physiologically structured populations bivariate collocation Numerical Analysis (math.NA) Dynamical Systems (math.DS) General Medicine stability of equilibria Computational Mathematics bivariate collocation infinitesimal generator partial differential equations stability of equilibria physiologically structured populations Modeling and Simulation FOS: Mathematics partial differential equations Mathematics - Numerical Analysis Mathematics - Dynamical Systems General Agricultural and Biological Sciences |
| Popis: | The asymptotic stability of the null equilibrium of a linear population model with two physiological structures formulated as a first-order hyperbolic PDE is determined by the spectrum of its infinitesimal generator. In this paper, we propose a general numerical method to approximate this spectrum. In particular, we first reformulate the problem in the space of absolutely continuous functions in the sense of Carathéodory, so that the domain of the corresponding infinitesimal generator is defined by trivial boundary conditions. Via bivariate collocation, we discretize the reformulated operator as a finite-dimensional matrix, which can be used to approximate the spectrum of the original infinitesimal generator. Finally, we provide test examples illustrating the converging behavior of the approximated eigenvalues and eigenfunctions, and its dependence on the regularity of the model coefficients. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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