High order analysis of nonlinear periodic differential equations
Abstract
In this letter we apply a method recently devised in aapla03 to find precise approximate solutions to a certain class of nonlinear differential equations. The analysis carried out in 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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