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

The objective 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 pseudoinverse 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.