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Approximate Analytical Solution for the Forced Korteweg‐de Vries Equation

Author

Listed:
  • Vincent Daniel David
  • Mojtaba Nazari
  • Vahid Barati
  • Faisal Salah
  • Zainal Abdul Aziz

Abstract

The forced Korteweg‐de Vries (fKdV) equations are solved using Homotopy Analysis Method (HAM). HAM is an approximate analytical technique which provides a novel way to obtain series solutions of such nonlinear problems. It has the auxiliary parameter ℏ, where it is easy to adjust and control the convergence region of the series solution. Some examples of forcing terms are employed to analyse the behaviours of the HAM solutions for the different fKdV equations. Finally, this form of HAM solution is compared with the analytical soliton‐type solution of fKdV equation as derived by Zhao and Guo. The results is found to be in good agreement with Zhao and Guo.

Suggested Citation

  • Vincent Daniel David & Mojtaba Nazari & Vahid Barati & Faisal Salah & Zainal Abdul Aziz, 2013. "Approximate Analytical Solution for the Forced Korteweg‐de Vries Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:795818
    DOI: 10.1155/2013/795818
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    1. Mojtaba Nazari & Faisal Salah & Zainal Abdul Aziz & Merbakhsh Nilashi, 2012. "Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Mojtaba Nazari & Faisal Salah & Zainal Abdul Aziz & Merbakhsh Nilashi, 2012. "Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, November.
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