High order analysis of nonlinear periodic differential equations

Details High order analysis of nonlinear periodic differential equations High order analysis of nonlinear periodic differential equations

2003-10-28

arxiv.org/abs/math-ph/0310060v2

Physics Letters A 327 (2004), 158-166

Physics

Mathematical Physics

14 pages, 13 figures

Scientific paper

10.1016/j.physleta.2004.05.016

In this letter we apply a method recently devised in \cite{aapla03} to find precise approximate solutions to a certain class of nonlinear differential equations. The analysis carried out in \cite{aapla03} is refined and results of much higher precision are obtained for the problems previously considered (Duffing equation, sextic oscillator). Fast convergence to the exact results is observed both for the frequency and for the Fourier coefficients. The method is also applied with success to more general polynomial potentials (the octic oscillator) and to the Van Der Pol equation.

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