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.


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