A Multilevel Wavelet Scheme for Evolution Equations with Time Adaptivity

The study in this paper is devoted to the stability and consistence analyses of an adaptive multilevel time discretization proposed by Bacry, Mallat and Papanicolau [1]. The main idea is to evolve the components in a multirresolution representation of the numerical solution by means of na explicit algorithm, adapting the time step according to each scale level. For a model problem, and in the context of biorthogonal wavelets, it is proved tha the stability condition and consistency order are the same as in the original non-adapted scheme.