Mohammad Zurigat, Asad A. Freihat and Ali H. Handam, The multi-step homotopy analysis method for solving the Jaulent-Miodek equations, Proyecciones Journal of Mathematics, 34 (1) (2015), 45-54.

n 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 modi fi cation 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 fi nding accurate approximate solutions to the corresponding problems. Thus, it is valid for both weakly and strongly nonlinear prob- lems. this work veri fi es 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.