Solution of the Duffing equation involving both integral and non-integral forcing terms

Numerical solutions of Duffing equations involving both integral and non-integral forcing terms

“…In this section, the proposed technique is applied to two Duffing equations and the obtained numerical results are compared with the corresponding experimental results obtained by the method presented in [9]. …”

“…However, the discussion on numerical solutions of Duffing equations such as (1.1) is little. Yao [9] presented an iterative reproducing kernel method for solving Duffing equation (1.1).…”

A pseudospectral method for nonlinear Duffing equation involving both integral and non‐integral forcing terms

“…For the purpose of comparison, in Table II, we compare the absolute error of our method with n D 12 and n D 16 together with the VIM given in [13] and an iterative reproducing kernel method given in [14]. In Table II, y n represent the nth term approximation obtained using VIM.…”

“…Geng [13] improved variational iteration method (VIM) for solving Equation (1). Also, Yao [14] presented an iterative reproducing kernel method for solving Equation (1).…”

Approximate Periodic Solutions for Oscillatory Phenomena Modelled by Nonlinear Differential Equations

“…The homotopy perturbation method (see, [1][2][3][4][5]), the variational formulation method (see, [5][6][7]), the harmonic balance methods (see, [8][9][10][11][12][13]), the quasilinearization technique (see, [14]), the reproducing kernel space method (see, [15]), the Adomian decomposition method (see, [16]), the parameter-expansion method (see, [17,18]), the variational iteration methods (see, [19][20][21]), the energy balance method (see, [20,22]), the amplitude-frequency formulation (see, [4,18]), the homotopy analysis method (see, [23][24][25]), the maxmin approach (see, [18]), the optimal homotopy asymptotic method (see, [26]), the residue harmonic balance method (see, [27]), the enhanced cubication method (see, [28]), the linearisation method (see, [29]), perturbation methods (see, [30]), and numerical methods (see, [31][32][33][34][35]).…”