Some New Analytical Techniques forDufting Oscillator with Very StrongNonlinearity

The current paper f ocuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of theequation of motion: the variational iteration method, He sparameter expanding method, parameterized perturbationmethod, and the homotopy p erturbation method.The results reveal that approximation obtained by these approaches are valid uniformly even f or very large parameters and are more accurate than straightforward expansion solution.The methods, which are proved to be mathematicalfy powerfultools for solving the nonlinear oscillators, can be easilyextended to any nonlinear equation, and the present paper canbe used as paradigms for many other applications in searchingfor periodic solutions, limit cycles or other approximatesolutions for real-life physics and engineering problems.