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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 705313, 8 pages
http://dx.doi.org/10.1155/2013/705313
Research Article

A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

Department of Mathematical Engineering, Chemical and Metallurgical Faculty, Yildiz Technical University, Esenler 34210, Istanbul, Turkey

Received 14 January 2013; Accepted 28 February 2013

Academic Editor: Adem Kiliçman

Copyright © 2013 Murat Osmanoglu and Mustafa Bayram. 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 have considered linear partial differential algebraic equations (LPDAEs) of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.