TY - JOUR ID - 1642 TI - The multi-step homotopy analysis method: A powerful scheme for handling non-linear oscillators JO - Iranian Journal of Science JA - ISTT LA - en SN - 2731-8095 AU - Zurigat, M. AU - Al-Shara, S. AU - Momani, S. AU - Alawneh, A. AD - Department of Mathematics, Al al-Bayt University, Mafraq, Jordan AD - Department of Mathematics, University of Jordan, Amman AD - Department of Mathematics, University of Jordan, Amman, Jordan Y1 - 2013 PY - 2013 VL - 37 IS - 3.1 SP - 421 EP - 429 KW - Non-linear oscillators KW - homotopy analysis method KW - numerical solutions DO - 10.22099/ijsts.2013.1642 N2 - 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. UR - https://ijsts.shirazu.ac.ir/article_1642.html L1 - https://ijsts.shirazu.ac.ir/article_1642_70909ef1ebb1fef861842127d76a1c61.pdf ER -