Application of wavelet transforms to the solution of boundary value problems for linear parabolic equations
A. A. Abbasov, O. A. Dyshin, Baghir Alakbar Suleimanov · Computational Mathematics and Mathematical Physics · 2008
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.