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Application of HAM to seventh order KdV equations

Author

Listed:
  • Rajan Arora

    (IIT Roorkee)

  • Hariom Sharma

    (IIT Roorkee)

Abstract

In this paper, the homotopy analysis method (HAM) is applied to obtain the approximate solutions of KdV equations of seventh order, which are Sawada Kotera Ito equation, Lax equation, and Kaup–Kuperschmidt equation, respectively. The convergence of the homotopy analysis method is discussed with the help of auxiliary parameter h, which controls the convergence of the method and also called as the convergence control parameter. The results obtained by the HAM are compared with the exact solutions, by fixing the value of arbitrary constant. It is found that HAM is very robust and elegant method, and by choosing a suitable value of h we can get the approximate solution in very few iteration. Computations are performed with the help of symbolic computation package MATHEMATICA.

Suggested Citation

  • Rajan Arora & Hariom Sharma, 2018. "Application of HAM to seventh order KdV equations," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(1), pages 131-138, February.
    • Handle: RePEc:spr:ijsaem:v:9:y:2018:i:1:d:10.1007_s13198-016-0490-7
    DOI: 10.1007/s13198-016-0490-7
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    Cited by:

    1. Rajeev Kumar & Rahul Dharra & Sanjeev Kumar, 2023. "Comparative qualitative analysis and numerical solution of conformable fractional derivative generalized KdV-mKdV equation," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(4), pages 1247-1254, August.
    2. Reem Alrebdi & Hind K. Al-Jeaid, 2023. "Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    3. Sidra Saleem & Malik Zawwar Hussain & Imran Aziz, 2021. "A reliable algorithm to compute the approximate solution of KdV-type partial differential equations of order seven," PLOS ONE, Public Library of Science, vol. 16(1), pages 1-17, January.

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