We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] 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.
@article{702934,
title = {Numerical approximation of density dependent diffusion in age-structured population dynamics},
booktitle = {Applications of Mathematics 2013},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2013},
pages = {88-97},
mrnumber = {MR3204433},
zbl = {1340.92046},
url = {http://dml.mathdoc.fr/item/702934}
}
Gerardo-Giorda, Luca. Numerical approximation of density dependent diffusion in age-structured population dynamics, dans Applications of Mathematics 2013, GDML_Books, (2013), pp. 88-97. http://gdmltest.u-ga.fr/item/702934/