title: The rapidly convergent solutions of strongly nonlinear oscillators.
abstract: 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.
authors.affiliation: Department of Mathematics, Rajshahi University of Engineering and Technology (RUET), Kazla, Rajshahi, 6204 Bangladesh.
authors.forename: M S
authors.initials: MS
authors.lastname: Alam
authors.affiliation: Department of Mathematics, Rajshahi University of Engineering and Technology (RUET), Kazla, Rajshahi, 6204 Bangladesh.
authors.forename: Md
authors.initials: M
authors.lastname: Abdur Razzak
authors.affiliation: Department of Mathematics, Rajshahi University of Engineering and Technology (RUET), Kazla, Rajshahi, 6204 Bangladesh.
authors.forename: Md
authors.initials: M
authors.lastname: Alal Hosen
authors.affiliation: Department of Mechanical Engineering, Rajshahi University of Engineering and Technology (RUET), Kazla, Rajshahi, 6204 Bangladesh.
authors.forename: Md
authors.initials: M
authors.lastname: Riaz Parvez
keywords: Duffing equation; Harmonic balance method; Nonlinear oscillation