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   -> Volume 4, Issue 12


Preprint: Wavelets adapted for boundary conditions
 
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monasse@matra-ms2i.fr (Pascal.Monasse)
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PostPosted: Fri Dec 06, 2002 9:37 am    
Subject: Preprint: Wavelets adapted for boundary conditions
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Preprint: Wavelets adapted for boundary conditions


Title : Orthonormal wavelet bases adapted for partial differential
equations with boundary conditions


Authors : Pascal Monasse & Valerie Perrier
pmonasse@lmd.ens.fr perrier@lmd.ens.fr


Abstract: We adapt ideas presented by Auscher to impose boundary
conditions on the construction of multiresolution analyses on the
interval, as introduced by Cohen, Daubechies and Vial. We construct
new orthonormal wavelet bases on the interval satisfying homogeneous
boundary conditions. This construction can be extanded to wavelet
packets, in the case of one boundary condition at each edge. We
present in detail the numerical computation of the filters and of the
derivative operators associated to these bases. We derive quadrature
formulae in order to study the approximation error at the edge of the
interval. Several examples illustrate the present construction.

Prepublications Mathematiques de l'Universite Paris-Nord, n. 95-11,
November 1995.

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