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

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 approximationin the regularization method is combined with the discrepancy principle. An error estimate is obtainedfor the stable approximate solution obtained by solving a set of linear algebraic equations for the waveletcoefficients of the desired solution.