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Numerical approximation of density dependent diffusion in age-structured population dynamics. (English) Zbl 1340.92046

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 88-97 (2013).
Summary: We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [C. Cusulin and the author, Numer. Methods Partial Differ. Equations 26, No. 2, 253–273 (2010; Zbl 1181.92080)] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result.
For the entire collection see [Zbl 1277.00032].

MSC:

92D25 Population dynamics (general)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs

Citations:

Zbl 1181.92080

Software:

Matlab
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