Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM

More accurate approximate analytical solution of pendulum with rotating support

“…The solution was compared with those presented by Ghafoori et al (2011) and Khan and Mirzabeigy (2014). All the results together with numerical solution (obtained by fourth-order Runge-Kutta formula) are presented in Table 1.…”

“…Harmonic balance method (Mickens, 1986;Lim et al, 2005;Belendez et al, 2006;Wu et al, 2006;Mickens, 2007;Alam et al, 2007;Belendez et al, 2009;Lai et al, 2009;Hosen et al, 2012) is a powerful method in which truncated Fourier series is used. Iterative homotopy harmonic balance (Guo and Leung, 2010), differential transformation (Ghafoori et al, 2011) and max-min (Yazdi et al, 2012) methods have been developed for solving strongly nonlinear oscillators. Energy balance method (He, 2002;Khan and Mirzabeigy, 2014;Alam et al, 2016;Mehdipour et al, 2010;Ebru et al, 2016;Zhang et al, 2009) is another widely used technique for solving strongly nonlinear oscillators.…”

“…Recently, EBM has been modified by truncating some higher order terms of the algebraic equations of related variables to the solution (Alam et al, 2016) and it measures more correct result than the usual method. Moreover, the modification on EBM used in Alam et al (2016) is valid for some nonlinear oscillators, especially when Ghafoori et al (2011) applying differential transformation method (DTM), Belendez et al (2006) using harmonic balance method and Yazdi et al (2012) using max-min approach. He (2002) first introduced energy balance method and Khan and Mirzabeigy (2014) was used to improve accuracy of He's energy balance method to obtain the solution of pendulum equation with rotating support.…”

Analyzing the nonlinear heat transfer equation by AGM

“…Recently, many new numerical techniques have been widely applied to the nonlinear problems. Some of these methods are Perturbation Method (PM) [1], Homotopy Perturbation Method (HPM) [2,3,4,5,6], Variational Iteration Method (VIM) [7,8,9], Homotopy Analysis Method (HAM) [10,11], Differential Transform Method (DTM) [12] and Adomian Decomposition Method (ADM) [13,14].…”

“…(4) to (9), so that (n + 1) unknown coefficients of Eq. (3) will be calculated for example a 0 , a 1 , a 2 a n .…”