Cattani, Carlo Haar wavelets based technique in evolution problems. (English) Zbl 1049.65103 Proc. Est. Acad. Sci., Phys. Math. 53, No. 1, 45-63 (2004). 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. Reviewer: Karel Najzar (Praha) Cited in 22 Documents MSC: 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35G10 Initial value problems for linear higher-order PDEs 65Y20 Complexity and performance of numerical algorithms 65T60 Numerical methods for wavelets Keywords:Haar wavelets; interpolation; differential operator; evolution problem; numerical example; reduction of complexity; algorithm; error bound; Haar transform PDFBibTeX XMLCite \textit{C. Cattani}, Proc. Est. Acad. Sci., Phys. Math. 53, No. 1, 45--63 (2004; Zbl 1049.65103)