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Periodic solutions of high accuracy to the forced Duffing equation: Perturbation series in the forcing amplitude
Published online by Cambridge University Press: 17 February 2009
Abstract
“Steady state” periodic solutions are sought to the forced Duffing equation. The solutions are expressed as formal Fourier series, giving rise to an infinite system of non-linear algebraic equations for the Fourier coefficients. This system is then solved using perturbation series in the amplitude of the forcing term. Solution profiles of high accuracy and phase-plane orbits are presented. The existence of limiting values of the forcing amplitude is discussed, and points of non-linear resonance are identified.
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- Copyright © Australian Mathematical Society 1987
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