Exact and approximate solutions for the anti-symmetric quadratic truly nonlinear oscillator
作者：
Highlights：
• The exact solution of the anti-symmetric quadratic truly nonlinear oscillator was expressed as a piecewise function.
• The Fourier coefficients of the exact solution were computed numerically and we showed these decrease rapidly.
• Using just a few of Fourier coefficients provides an accurate analytical representation of the exact periodic solution.
• Analytical approximate solutions are built up containing only two harmonics as well as a rational harmonic representation.
• The two-harmonic representation is more accurate than the rational harmonic representation.
摘要
•The exact solution of the anti-symmetric quadratic truly nonlinear oscillator was expressed as a piecewise function.•The Fourier coefficients of the exact solution were computed numerically and we showed these decrease rapidly.•Using just a few of Fourier coefficients provides an accurate analytical representation of the exact periodic solution.•Analytical approximate solutions are built up containing only two harmonics as well as a rational harmonic representation.•The two-harmonic representation is more accurate than the rational harmonic representation.
论文关键词：Nonlinear oscillators,Conservative systems,Truly oscillators,Fourier series expansion,Approximate solutions,Symbolic computation
论文评审过程：Available online 3 September 2014.
论文官网地址：https://doi.org/10.1016/j.amc.2014.08.005
