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Haar wavelets based technique in evolution problems. (English) Zbl 1049.65103
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.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35G10Initial value problems for linear higher-order PDE
65Y20Complexity and performance of numerical algorithms
65T60Wavelets (numerical methods)