Mohammad Zurigat, Safwan Al-Shara, Shaher Momani and Ahmad Alawneh, The multi-step homotopy analysis method: A powerful scheme for handling non-linear oscillators, Iranian Journal of Science and Technology, 37 (2013), 421-429.

This paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (MSHAM). The proposed scheme is onl y a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequen ce of small intervals (i.e. tim e step) for finding accurate approximate solutions to the corresponding problems. Severa l illustrative examples are given to demonstrate the effectiveness of the present method. Figurative comparis ons between the MSHAM and the classical fourth-order Runge-Kutta method (RK4) reveal th at this modified method is very effective and convenient.