Towards a method for solving partial differential equations by using wavelet packet bases

Abstract In this paper we present a new methodology based on the wavelet packet concept, in order to define an adaptive method for the approximation of partial differential equations. The wavelet packet framework allows us to define the notion of a minimal basis that has proven to be an efficient procedure for data compression. The purpose here is to take benefit of this compression to represent accurately and economically the solution of a time dependent PDE. The time discretization is a standard multistep scheme. The spacial discretization is defined by inferring a reduced basis for the solution at the new time step, from the knowledge of the previous ones.