Harmonic Wavelet Solution ofPoisson's Problem

The multiscale (wavelet) decomposition of the solution is proposed for the analysis of the Poisson problem. The approximate so- lution is computed with respect to a ¯nite dimensional wavelet space [4, 5, 7, 8, 16, 15] by using the Galerkin method. A fundamental role is played by the connection coe±cients [2, 7, 11, 9, 14, 17, 18], expressed by some hypergeometric series. The solution of the Poisson problem is compared with the approach based on Daubechies wavelets [18]

Harmonic wavelet solution of Poisson's problem with a localized source

A method, based on a multiscale (wavelet) decomposition of the solution is proposed for the analysis of the Poisson problem. The solution is approximated by a finite series expansion of harmonic wavelets and is based on the computation of the connection coefficients. It is shown, how a sourceless Poisson's problem, solved with the Daubechies wavelets, can also be solved in presence of a localized source in the harmonic wavelet basis

Wave Propagation of Shannon Wavelets

The problem of the evolution of solitary profile having the form of a Shannon wavelet is considered as solution of a generalization of the Burger equation. Some nonlinear effects such as the breaking down of the wave into localized chaotic oscillations are shown