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Zbl 1049.65103
Cattani, Carlo
Haar wavelets based technique in evolution problems. (English)
[J] Proc. Est. Acad. Sci., Phys. Math. 53, No. 1, 45-63 (2004). ISSN 1406-0086

The compression property of wavelets in the analysis of an evolution problem is investigated. The effectiveness of wavelets both in the reduction of complexity and in better approximation is shown. Haar wavelets are used for defining the wavelet solution of an evolution (parabolic-hyperbolic) problem. A numerical derivative algorithm is also defined. As application, the heat propagation (of an initial square wave) is explicitly given in terms of wavelets.
[Karel Najzar (Praha)]

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35G10 Initial value problems for linear higher-order PDE
65Y20 Complexity and performance of numerical algorithms
65T60 Wavelets

Keywords: Haar wavelets; interpolation; differential operator; evolution problem; numerical example; reduction of complexity; algorithm; error bound; Haar transform

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