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Numerical computation of forced oscillations in coupled duffing equations

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Abstract

Oscillating phenomena in non-linear mechanical systems with two degrees of freedom described by coupled Duffing equations are studied from the computational view point. Galerkin approximations of order 7 are computed with a very high precision on an electronic computer by applying a numerical approximation method of Urabe for the Galerkin method. The existence of an exact isolated periodic solution in a small neighborhood of these Galerkin approximations is proved and the error bound of these Galerkin approximations is given. The stability of Stierel's integration method in combination with Galerkin approximations is shown.

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  1. Department of Rational Mechanics, Faculty of Applied Sciences, Free University of Brussels, Belgium

    René van Dooren

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  1. René van Dooren
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van Dooren, R. Numerical computation of forced oscillations in coupled duffing equations. Numer. Math. 20, 300–311 (1972). https://doi.org/10.1007/BF01407372

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