Global residue harmonic balance method for Helmholtz–Duffing oscillator

In this paper, an improved harmonic balance method was proposed to solve the Duffing-harmonic equation. This method is called the global residue harmonic balance method (GRHBM). Unlike other harmonic balance methods, all the former global residual errors are introduced in the present approximation to improve the accuracy. A maximum absolute value of the relative errors for the second-order approximation is less than 0.1165%. Comparison of the result obtained using this approach with the exact one and existing results reveals that the high accurate, simplicity and efficiency of the proposed procedure. The method can be easily extended to other strongly nonlinear oscillators.