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

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  • Younghae Do
  • Bongsoo Jang

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.

Suggested Citation

  • Younghae Do & Bongsoo Jang, 2012. "Nonlinear Klein‐Gordon and Schrödinger Equations by the Projected Differential Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:150527
    DOI: 10.1155/2012/150527
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    References listed on IDEAS

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    1. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    2. Younghae Do & Bongsoo Jang, 2012. "Enhanced Multistage Differential Transform Method: Application to the Population Models," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    7. Zhang, Huiqun, 2007. "New exact Jacobi elliptic function solutions for some nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 653-660.
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