Error Estimates for Harmonic-Balance Solutions of Nonlinear Dynamical Systems (original) (raw)

This paper presents an a posteriori error estimate for harmonic balance solutions of nonlinear dynamical systems, specifically focusing on their steady-state response to periodic excitation. The study evaluates the performance of the error estimate through examples involving a Duffing equation and a Coulomb-damped system. Comparisons with RMS errors obtained from time integration demonstrate that the proposed error estimate is easy to calculate and provides reliable accuracy assessments, particularly for the Duffing equation. The research emphasizes the importance of adaptive solution techniques in determining the necessary number of harmonics to achieve specified accuracy levels.