Numerical analysis for a three interacting species model with nonlocal and cross diffusion
Résumé
In this paper, we consider a reaction-di usion system describing three interacting species in the food chain structure with nonlocal and cross di usion. We propose a semi implicit fi nite volume scheme for this system, we establish existence and uniqueness of the discrete solution, and it is also showed that the discrete solution generated by the given scheme converges to the corresponding weak solution for the model studied. The convergence proof is based on the use of the discrete Sobolev embedding inequalities with general boundary conditions and a space-time L1 compactness argument that mimics the compactness lemma due to S. N. Kruzhkov. Finally we give some numerical examples.