Identification of Asymptotic Decay to Self-Similarity for One-Dimensional Filtration Equations

Abstract. The concern of this paper is the derivation and the analysis of a simple explicit numerical scheme for general one-dimensional filtration equations. It is based on an alternative formulation of the problem using the pseudo-inverse of the density’s repartition function. In particular, the numerical approximations can be proven to satisfy a contraction property for a Wasserstein metric. Various numerical results illustrate the ability of this numerical process to capture the time-asymptotic decay towards self-similar solutions even for fast-diffusion equations.