Unified overview of wavelet-based methods for differential equations
Sônia M. Gomes · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1997
There exists a great variety of numerical methods to solve differential equations. With the advent of wavelet analysis, new approaches have been tried: the wavelet-based methods. One of the main points in this kind of approach is the use of the multi-resolution structure of wavelet bases to reduce the number of degrees of freedom needed to represent the approximate solutions. Wavelet-based methods usually use Galerkin, Petrov-Galerkin or even collocation schemes. We discuss here a unified framework for analyzing the performance of these different schemes. It uses the concepts of restriction and prolongation operators. Using this formalism, we give an overview of some recent results on the representation of differential operators in the wavelet context.