Application of Wavelet Transforms to the Solution of Boundary Value Problems for Linear Parabolic Equations

被引：9

作者：

Abbasov, E. M. ^{[1
]}

Dyshin, O. A. ^{[1
]}

Suleimanov, B. A. ^{[1
]}

机构：

[1] Neftegasproekt, Baku 370112, Azerbaijan

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2008年 / 48卷 / 02期

关键词：

weak solutions to initial-boundary value problems; linear parabolic equations; distributional derivative; wavelet transform; multiresolution analysis; finite-dimensional approximation scheme;

D O I：

10.1134/S0965542508020085

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：251 / 268

页数：18

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