Analytical approximate solutions of nonlinear oscillators by the modified decomposition method

Analytical approximate solutions for the nonlinear oscillators of the form cursive Greek chï + c₁cursive Greek chi = ε f (cursive Greek chi, cursive Greek chi̇) are derived using the modified decomposition method. The analytical solutions of our model equations are calculated in the form of convergent series with easily computable components. Then the Laplace transformation and Padè approximant are effectively used to improve the convergence rate and accuracy of the computed series. The validity of the solutions is verified through some numerical examples. The results compare well with those obtained by the Runge-Kutta, fourth-order method. The proposed scheme avoids the complexity provided by perturbation techniques.