Numerical Algorithms for a Variational Problem of the Spatial Segregation of Reaction-Diffusion Systems

In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both solutions and free boundaries to derive our scheme. Furthermore, the proof of convergence of the numerical method is given in some particular cases. We also apply our numerical simulations for the spatial segregation limit of diffusive Lotka-Volterra models in presence of high competition and inhomogeneous Dirichlet boundary conditions. We discuss numerical implementations of the resulting approach and present computational tests

The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme

In this work we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the equivalence of the new formulation to the traditional one. We define consistent numerical schemes for approximating infinity ground states and higher eigenfunctions and perform numerical experiments which also shed light on some open conjectures in the field.Comment: 20 pages, 8 figure