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Abstract and Applied Analysis
Volume 2012, Article ID 682752, 31 pages
Research Article

Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition

Department of Mathematics, Trakya University, 22030 Edirne, Turkey

Received 21 February 2012; Accepted 28 March 2012

Academic Editor: Allaberen Ashyralyev

Copyright © 2012 Deniz Agirseven. 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.


Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. A procedure of modified Gauss elimination method is used for the solution of these difference schemes. Homotopy analysis method is applied. Comparison of finite difference and homotopy analysis methods is given on the problem.