Application of variational iteration method to free vibration analysis of a tapered beam mounted on two-degree of freedom subsystems

Analytical solutions of nonlinear oscillator with coordinate-dependent mass and Euler–Lagrange equation using the parameterized homotopy perturbation method

“…Over the years, different solution techniques have been established. These include the homotopy perturbation method (HPM), [1][2][3][4][5][6] energy balance method, [7][8][9][10] amplitude-frequency formulation, 11,12 variational iteration method, [13][14][15][16][17][18] and parameter expanding method. 19,20 The HPM given by He et al [1][2][3][4][5] is applied to provide solutions to differential and integral equations-linear and nonlinear.…”

Explicit Solutions for the (2 + 1)-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain

“…Analytical solutions for these equations are obtained using the homotopy perturbation method, Darboux transformation, variational iteration, Painlevé expansions, the homogeneous balance method, the Jacobi elliptic function, the exp-function method, and extended tanh-function [4][5][6][7][8][9][10][11][12][13]. The (2 + 1)-dimensional Jaulent-Miodek (JM) evolution equation is a highly nonlinear partial differential, previously solved analytically using several methods such as Hirota's bilinear method [14], leading to a multiple-soliton solution of this equation.…”

A new modification of the homotopy perturbation method

“…Efforts to overcome these difficulties have led to formulation of several analytical and approximate techniques. Some of these techniques include non-perturbative method, [1][2][3][4][5] weighted linearization, 6 Adomian decomposition, [7][8][9][10][11][12][13][14] variational iteration, [15][16][17][18][19][20] energy balance, [21][22][23] tanh, [24][25][26] F-expansion, 27,28 and homotopy perturbation methods. [29][30][31][32][33][34] Most of the methods have recorded recent advancements and improvements, as evidenced in the homotopy perturbation method.…”