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Jang, Bongsoo
Computational Mathematical Science Lab (CMS Lab)
Research Interests
  • Numerical analysis, dynamics, fractional systems, data sciences

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

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Title
Nonlinear Klein-Gordon and Schrodinger Equations by the Projected Differential Transform Method
Author
Do, YounghaeJang, Bongsoo
Keywords
HOMOTOPY PERTURBATION METHOD; VARIATIONAL ITERATION METHOD; TRAVELING-WAVE SOLUTIONS; INITIAL-VALUE PROBLEMS; F-EXPANSION METHOD; DECOMPOSITION METHOD; EVOLUTION-EQUATIONS; SYSTEMS
Issue Date
2012
Publisher
HINDAWI PUBLISHING CORPORATION
Citation
ABSTRACT AND APPLIED ANALYSIS, v.2012, no., pp.1 - 15
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 Schrodinger 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.
URI
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DOI
http://dx.doi.org/10.1155/2012/150527
ISSN
1085-3375
Appears in Collections:
SNS_Journal Papers
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