Modified Lindstedt–Poincare methods for some strongly non-linear oscillations

Hagedorn, 1981 Mickens, 1981 Nayfeh, 1985 Nayfeh, 1979 He, 2000, A review on some new recently developed nonlinear analytical techniques, Int. J. Non-linear Sci. Numer. Simulation, 1, 51, 10.1515/IJNSNS.2000.1.1.51 Cheung, 1991, A modified Lindstedt–Poincare method for certain strongly nonlinear oscillators, Int. J. Non-Linear Mech., 26, 367, 10.1016/0020-7462(91)90066-3 Dai, 1990, Approximate analytical solutions for some strongly nonlinear problems, Sci. China Ser. A, 2, 153 He, 1998, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engng., 167, 57, 10.1016/S0045-7825(98)00108-X He, 1998, Approximate solution for nonlinear differential equations with convolution product nonlinearities, Comput. Methods Appl. Mech. Engng., 167, 69, 10.1016/S0045-7825(98)00109-1 He, 1999, Variational iteration method: a kind of nonlinear analytical technique: some examples, Int. J. Non-linear Mech., 34, 699, 10.1016/S0020-7462(98)00048-1 He, 1999, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engng., 178, 257, 10.1016/S0045-7825(99)00018-3 He, 2000, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Non-linear Mech., 35, 37, 10.1016/S0020-7462(98)00085-7 He, 1999, Some new approach to Duffing equation with strongly & high order non-linearity (I) linearized perturbation technique, Commun. Nonlinear Sci. Numer. Simulation, 4, 78, 10.1016/S1007-5704(99)90064-3 He, 1999, Analytical solution of a nonlinear oscillator by the linearized perturbation technique, Commun. Nonlinear Sci. Numer. Simulation, 4, 103, 10.1016/S1007-5704(99)90021-7 He, 2000, A new perturbation technique which is also valid for large parameters, J. Sound Vib., 229, 1257, 10.1006/jsvi.1999.2509 He, 1999, Some new approach to Duffing equation with strongly & high order nonlinearity (II) parameterized perturbation technique, Commun. Nonlinear Sci. Numer. Simulation, 4, 81, 10.1016/S1007-5704(99)90065-5 J.R. Acton, P.T. Squire, Solving Equations with Physical Understanding, Adam Hilger Ltd., Bristol and Boston, 1985.