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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

Lawrence K. Forbes
Lawrence K. Forbes
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Queensland 4067, Australia.
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Abstract

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“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.

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 1 , July 1987 , pp. 21 - 38
Copyright
Copyright © Australian Mathematical Society 1987

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