Nonlinear Klein-Gordon and Schrodinger Equations by the Projected Differential Transform Method
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- Nonlinear Klein-Gordon and Schrodinger Equations by the Projected Differential Transform Method
- Do, Younghae; Jang, Bongsoo
- HOMOTOPY PERTURBATION METHOD; VARIATIONAL ITERATION METHOD; TRAVELING-WAVE SOLUTIONS; INITIAL-VALUE PROBLEMS; F-EXPANSION METHOD; DECOMPOSITION METHOD; EVOLUTION-EQUATIONS; SYSTEMS
- Issue Date
- HINDAWI PUBLISHING CORPORATION
- ABSTRACT AND APPLIED ANALYSIS, v.2012, no., pp.1 - 15
- 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.
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