Cattani, Carlo
(2002)
*Wavelet solutions of evolution problems.*
Accademia Peloritana dei Pericolanti - Classe di Scienze FF.MM.NN., LXXX (1).
pp. 21-34.

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## Abstract

In the following is given a method [2 10] for representing partial differential (evolution) operators using Haar wavelet bases [8, 10, 12]- Since the Haar wavelets are not smooth, they are regularized using auxiliary polynomial splines and defining suitable discrete operators [8, 3] acting on the spaces of the piecewise functions $V_n \subset L^2(lR)$. Thus the projection of the partial differential operators is done into the Spline-Haar Space, subspace of $V_n$, obtaining discrete operators. Althought these discrete operators depend both on the order of the splines and on the space resolution level [12], they are univocally defined (with respect to the projection) in the Spline-Haar Space. A comparison of the approximate wavelet solution with a classical problem of heat propagation is also given.

Item Type: | Article |
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Subjects: | M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali > 2002 M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Giuridiche, Economiche e Politiche > 2002 M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Lettere Filosofia e belle Arti > 2002 |

Depositing User: | Dr PP C |

Date Deposited: | 19 Sep 2012 09:26 |

Last Modified: | 20 Sep 2012 07:42 |

URI: | http://cab.unime.it/mus/id/eprint/618 |

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