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Abstract and Applied Analysis
Volume 2012, Article ID 738346, 11 pages
http://dx.doi.org/10.1155/2012/738346
Research Article

Solution of Second-Order IVP and BVP of Matrix Differential Models Using Matrix DTM

1Young Researchers Club, Ardabil Branch, Islamic Azad University, P.O. Box 56169-54184, Ardabil, Iran
2Department of Mathematics, Universiti Putra Malaysia (UPM), 43400, Serdang, Malaysia

Received 2 February 2012; Accepted 29 February 2012

Academic Editor: Irena Lasiecka

Copyright © 2012 Reza Abazari and Adem Kılıcman. 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 introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by 𝐮 ( 𝑡 ) = 𝑓 ( 𝑡 , 𝐮 ( 𝑡 ) , 𝐮 ( 𝑡 ) ) and subject to initial conditions 𝐮 ( 𝑎 ) = 𝐮 0 , 𝐮 ( 𝑎 ) = 𝐮 1 and boundary conditions 𝐮 ( 𝑎 ) = 𝐮 0 , 𝐮 ( 𝑏 ) = 𝐮 1 , where 𝐮 0 , 𝐮 1 𝑅 𝑟 × 𝑞 . Also the convergence of present method is established. Several illustrative examples are given to demonstrate the effectiveness of the present method.