This paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (MSHAM). The proposed scheme is only a simple modification of the homotopy analysis method, 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. Several illustrative examples are given to demonstrate the effectiveness of the present method. Figurative comparisons between the MSHAM and the classical fourth-order Runge-Kutta method (RK4) reveal that this modified method is very effective and convenient.
Zurigat, M., Al-Shara, S., Momani, S., & Alawneh, A. (2013). The multi-step homotopy analysis method: A powerful
scheme for handling non-linear oscillators. Iranian Journal of Science, 37(3.1), 421-429. doi: 10.22099/ijsts.2013.1642
MLA
M. Zurigat; S. Al-Shara; S. Momani; A. Alawneh. "The multi-step homotopy analysis method: A powerful
scheme for handling non-linear oscillators", Iranian Journal of Science, 37, 3.1, 2013, 421-429. doi: 10.22099/ijsts.2013.1642
HARVARD
Zurigat, M., Al-Shara, S., Momani, S., Alawneh, A. (2013). 'The multi-step homotopy analysis method: A powerful
scheme for handling non-linear oscillators', Iranian Journal of Science, 37(3.1), pp. 421-429. doi: 10.22099/ijsts.2013.1642
VANCOUVER
Zurigat, M., Al-Shara, S., Momani, S., Alawneh, A. The multi-step homotopy analysis method: A powerful
scheme for handling non-linear oscillators. Iranian Journal of Science, 2013; 37(3.1): 421-429. doi: 10.22099/ijsts.2013.1642
)