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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 150527, 15 pages
http://dx.doi.org/10.1155/2012/150527
Research Article

Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method

1Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea
2Ulsan National Institute of Science and Technology (UNIST), Ulsan Metropolitan City 689-798, Republic of Korea

Received 12 April 2012; Accepted 21 June 2012

Academic Editor: Elena Litsyn

Copyright © 2012 Younghae Do and Bongsoo Jang. 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

The differential transform method (DTM) is based on the Taylor series for all variables, but it differs from the traditional Taylor series in calculating coefficients. Even if the DTM is an effective numerical method for solving many nonlinear partial differential equations, there are also some difficulties due to the complex nonlinearity. To overcome difficulties arising in DTM, we present the new modified version of DTM, namely, the projected differential transform method (PDTM), for solving nonlinear partial differential equations. The proposed method is applied to solve the various nonlinear Klein-Gordon and Schrödinger equations. Numerical approximations performed by the PDTM are presented and compared with the results obtained by other numerical methods. The results reveal that PDTM is a simple and effective numerical algorithm.