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2012 Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method
Younghae Do, Bongsoo Jang
Abstr. Appl. Anal. 2012: 1-15 (2012). DOI: 10.1155/2012/150527


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.


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Younghae Do. Bongsoo Jang. "Nonlinear Klein-Gordon and Schrödinger Equations by the Projected Differential Transform Method." Abstr. Appl. Anal. 2012 1 - 15, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1246.65235
MathSciNet: MR2959742
Digital Object Identifier: 10.1155/2012/150527

Rights: Copyright © 2012 Hindawi


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