International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

The Solution of Nonlinear Klein - Gordon Equation using Reduced Differential Transform Method

    ,

Author Affiliations

  • 1Physical and Theoretical Chemistry Group, Department of Pure and Applied Chemistry, University of Calabar, Calabar, NIGERIA
  • 2 Department of Mathematics and Statistics, Ngoundere University, CAMEROON

Res. J. Physical Sci., Volume 1, Issue (1), Pages 21-23, February,4 (2013)

Abstract

In this paper, a seemingly new mathematical technique, the reduced differential transform method (RDTM) has been applied to solve the nonlinear Klein - Gordon equation of the form: utt – uxx = –u2 + f(t) subject to the general initial conditions. The results indicate this method (RDTM) to be very effective and simple. It is also consistent with the homotopy analysis method (HAM).

References

  1. Alomari A. K., Mohd Salami MD. N. and Roslinda M. N., Approximate Analytical Solutions of the Klein – Gordon Equation by means of the Homotopy Analysis Method, Journal of Quality Measurement and Analysis,, 45 – 57 (2008)
  2. Gokdogan A., Merdan M. and Yildirim A., Differential Transform Method for solving a Neutral Functional-Differential Equation with Proportional Delays, Caspian Journal of Mathematical Sciences, 27–33 (2007)
  3. Keskin Y. and Otutanc G., Reduced Differential Transform Method for Generalized KdV Equations, Mathematics and Computer Application, 15, 382–393 (2010)
  4. Keskin Y., Caglar I. and Koc A.B., Numerical Solution of Sine – Gordon Equation by Reduced Differential Transform Method, Proceedings of the World Congress on Engineering, July 6 – 8, London, U.K., (2011)
  5. Keskin Y. and Oturanc G., Numerical Solution of Regularized Long Wave Equation by Reduced Differential Transform Method, Applied Mathematical Sciences, 1221–1231 (2010)
  6. Abazari R., Numerical Simulation of Coupled Nonlinear Schrodinger Equation by RDTM and Comparison with DTM, Journal of AppliedSciences, 11, 3454–3463 (2011)
  7. Secer A., Solving Time – Frational Reaction – Diffusion Equation by Reduced Differential Transform Method, International Journal of Computer Science in Emerging Technology, 19–22 (2012)
  8. Arora R., Siddiqui M.J. and Singh V.P., Solution of the Modified Equal Width Equation, its Variant and Non – homogeneous Burger’s Equation by RDT method, American Journal of Computational and Applied Mathematics,, 53–56 (2011)
  9. Keskin Y. and Oturanc G., Application of Reduced Differential Transformation Method for solving Gas Dynamics Equation, International Journal of Contemporary Mathematical sciences, 1091–1096 (2010)
  10. Keskin Y., Servi S. and Oturanc G., Reduced Differential Transform Method for solving Klein – Gordon Equations, Proceedings of the World Congress on Engineering, July 6 – 8, London, U.K. (2011)
  11. Keskin Y., Oturanc G., Reduced Differential Transform for Solving Linear and Nonlinear Wave Equations, Iranian Journal of Science and Technology, Transaction A, 34, 113–122 (2010)
  12. Taghizadeh N., Akbari M., Shahidi M., Application of Reduced Differential Transform Method to the Wu – Zhang Equation, Australian Journal of Basic and Applied Sciences, 565–571 (2011)
  13. Taha B., The use of Reduced Differential Transform Method for Solving Partial Differential Equations with Variable Coefficients, Journal of Basrah Research (Sciences),37, 226–233 (2011)