Wavelets and distributed approximating functionals

Guo-Wei Wei

doi:10.1016/S0010-4655(98)00051-4

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Wavelets and distributed approximating functionals

1998-07-01

PRE

Guo-Wei Wei *

Donald J. Kouri

David K. Hoffman

DOI：10.1016/S0010-4655(98)00051-4

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Abstract

En 中文

A general procedure is proposed for constructing father and mother wavelets that have excellent time-frequency localization and can be used to generate entire wavelet families for use as wavelet transforms. One interesting feature of our father wavelets (scaling functions) is that they belong to a class of generalized delta sequences, which we refer to as distributed approximating functionals (DAFs). We indicate this by the notation wavelet-DAFs. Correspondingly, the mother wavelets generated from these wavelet-DAFs are appropriately called DAF-wavelets. Wavelet-DAFs can be regarded as providing a pointwise (localized) spectral method, which furnishes a bridge between the traditional global methods and local methods for solving partial differential equations. They are shown to provide extremely accurate numerical solutions for a number of nonlinear partial differential equations, including the Korteweg-de Vries (KdV) equation, for which a previous method has encountered difficulties (J. Comput. Phys. 132 (1997) 233). (C) 1998 Elsevier Science B.V.

Keywords:

distributed approximating functional (DAF)

Dirichlet-Gabor DAF-wavelet

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