The multi-step homotopy analysis method for solving the Jaulent-Miodek equations

• Zurigat, Mohammad ^[1] ; Freihat, Asad A. ^[2] ; Handam, Ali H.
  1. [1] Al al-Bayt University

     Al al-Bayt University

     Jordania

     
  2. [2] Al-Balqa` Applied University

     Al-Balqa` Applied University

     Jordania

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 34, Nº. 1, 2015, págs. 45-54
• Idioma: inglés
• DOI: 10.4067/S0716-09172015000100004
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• Resumen

  • In this work, the multi-step homotopy analysis method (MHAM) is applied to obtain the explicit analytical solutions for system of the Jaulent Miodek equations. The proposed scheme is only a simple modification of the homotopy analysis method (HAM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. Thus, it is valid for both weakly and strongly nonlinear problems. this work verifies the validity and the potential of the MHAM for the study of nonlinear systems. A comparative study between the new algorithm and the exact solution is presented graphically. convenient.

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