The compression property of wavelets in the analysis of an evolution problem (with unsmooth initial conditions) is investigated. The effectiveness of wavelets both in the reduction of complexity (number of coefficients) and in better approximation is shown. Haar wavelets, having the simplest interpretation of the wavelet coefficients, are used for defining the wavelet solution of an evolution (parabolic-hyperbolic) problem. The approximate solution, at a given fixed scale (resolution), results from the superimposition of (a small set of) fundamental wavelets, thus giving (also) a physical interpretation to wavelets. Since Haar wavelets are not smooth enough, a numerical derivative algorithm, which allows the scale approximation of partial differential evolution operators, is also defined. As application, the heat propagation (of an initial square wave) is explicitly given in terms of wavelets.

Haar wavelets based technique in evolution problems

CATTANI, Carlo
2004

Abstract

The compression property of wavelets in the analysis of an evolution problem (with unsmooth initial conditions) is investigated. The effectiveness of wavelets both in the reduction of complexity (number of coefficients) and in better approximation is shown. Haar wavelets, having the simplest interpretation of the wavelet coefficients, are used for defining the wavelet solution of an evolution (parabolic-hyperbolic) problem. The approximate solution, at a given fixed scale (resolution), results from the superimposition of (a small set of) fundamental wavelets, thus giving (also) a physical interpretation to wavelets. Since Haar wavelets are not smooth enough, a numerical derivative algorithm, which allows the scale approximation of partial differential evolution operators, is also defined. As application, the heat propagation (of an initial square wave) is explicitly given in terms of wavelets.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/1067210
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact