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Biorthogonal wavelets and approximations of operators
Author(s) -
Guichaoua M.,
Liandrat J.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20000801307
Subject(s) - biorthogonal system , wavelet , biorthogonal wavelet , mathematics , stability (learning theory) , multiresolution analysis , scheme (mathematics) , wavelet transform , approximations of π , legendre wavelet , mathematical analysis , algorithm , computer science , discrete wavelet transform , artificial intelligence , machine learning
We present an explicit scheme, based on wavelets, for the approximation of evolution equations of type δ U /δ t / + δ/δ x ( f ( U )) = 0. It is constructed using a Taylor scheme for the time approximation and a wavelet method for spatial approximation. This scheme is shown to be stable and convergent under a specific stability condition and can be implemented fast on c‐structured wavelet spaces of approximation thanks to the introduction of scheme dependant biorthogonal multiresolution analyses. A scale dependent time step version is presented that allows a strong reduction of complexity. For discontinuous solutions, a non linear version has been proposed and numerically tested.