The rapidly convergent solutions of strongly nonlinear oscillators

Based on the harmonic balance method (HBM), an approximate solution is determined from the integral expression (i.e., first order differential equation) of some strongly nonlinear oscillators. Usually such an approximate solution is obtained from second order differential equation. The advantage of the new approach is that the solution converges significantly faster than that obtained by the usual HBM as well as other analytical methods. By choosing some well known nonlinear oscillators, it has been verified that an n-th (n ≥ 2) approximate solution (concern of this article) is very close to (2n − 1)-th approximations obtained by usual HBM.