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

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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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     title = {Application of wavelet transforms to the solution of boundary value problems for linear parabolic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_2_a7/}
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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/