Higher accuracy analytical approximations to the Duffing-harmonic oscillator

A new method has been presented for analytically solving the Duffing-harmonic oscillator. The method is obtained by combining Newton's method with the harmonic balance method. By using the method, one obtains linear algebraic equations instead of nonlinear algebraic equations. The complexity of the HB method is greatly simplified. Iteration of procedure yields rapid convergence with respect to exact solution. The results are valid for the complete range of oscillation amplitude, including the limiting cases of amplitude approaching zero and infinity.