Geodesic
Application of wavelet transforms to the solution of boundary value problems for linear parabolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 2, pp. 264-281 
E. M. Abbasov; O. A. Dyshin; B. A. Suleimanov. Application of wavelet transforms to the solution of boundary value problems for linear parabolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 2, pp. 264-281. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_2_a7/
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     title = {Application of wavelet transforms to the solution of boundary value problems for linear parabolic equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A method based on wavelet transforms is proposed for finding weak solutions to initial-boundary value problems for linear parabolic equations with discontinuous coefficients and inexact data. In the framework of multiresolution analysis, the general scheme for finite-dimensional approximation in the regularization method is combined with the discrepancy principle. An error estimate is obtained for the stable approximate solution obtained by solving a set of linear algebraic equations for the wavelet coefficients of the desired solution.

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