In this paper, we propose an auto adaptive time-step finite volume scheme for a class of two-time reaction-diffusion models of spatially structured population dynamics. Under specific assumptions, we prove that the privileged scheme preserves, at the discrete level, the main features of the continuous problem, namely the non-negativity of the solutions, monotonicity and boundedness. Finally, we present some numerical results to illustrate the efficiency of the proposed algorithm and the behaviour of the model and of the scheme.
Digital Object Identifier (DOI)
El Harrak, A. and Bergam, A.
"Preserving Finite-Volume Schemes for Two-Time Reaction-Diffusion Model,"
Applied Mathematics & Information Sciences: Vol. 14
, Article 5.
Available at: https://dc.naturalspublishing.com/amis/vol14/iss1/5