Wavelets, PDEs and numerical analysis

Abstract

The paper presents various drawbacks in the Fourier analysis of solutions of partial differential equations. Wavelets are gradually introduced and some of their seducing properties are presented. In particular, it is shown how some of the difficultles associated with Fourier analysis can be overcome. After highlighting the success of wavelets, this work speculates on the use of wavelets in making further progress in the analysis of solutions and their numerical approximation.