Wavelet-Galerkin method for solving parabolic equations in finite domains

A novel wavelet-Galerkin method tailored to solve parabolic equations in fi nite domains is presented. The emphasis of the paper is on the development of the discretization formulations that are specific to finite domain parab olic equations with arbitrary boundary conditions based on weak form functi onals. The proposed method also deals with the development of algorithms fo r computing the associated connection coefficients at arbitrary points. Her e the Lagrange multiplier method is used to enforce the essential boundary conditions. The numerical results on a two-dimensional transient heat condu cting problem are used to validate the proposed wavelet-Galerkin algorithm as an effective numerical method to solve finite domain parabolic equations . (C) 2001 Elsevier Science B.V. All rights reserved.