Table of Contents
Journal of Computational Engineering
Volume 2014, Article ID 346731, 12 pages
http://dx.doi.org/10.1155/2014/346731
Research Article

Wavelet Method for Numerical Solution of Parabolic Equations

Department of Mathematics, Srikishan Sarda College, Hailakandi 788151, India

Received 18 April 2013; Accepted 4 December 2013; Published 27 February 2014

Academic Editor: Fu-Yun Zhao

Copyright © 2014 A. H. Choudhury. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We derive a highly accurate numerical method for the solution of parabolic partial differential equations in one space dimension using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method using some special types of basis functions obtained by integrating Daubechies functions which are compactly supported and differentiable. The time variable is discretized by using various classical finite difference schemes. Theoretical and numerical results are obtained for problems of diffusion, diffusion-reaction, convection-diffusion, and convection-diffusion-reaction with Dirichlet, mixed, and Neumann boundary conditions. The computed solutions are highly favourable as compared to the exact solutions.