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A theoretical basis for the Harmonic Balance Method
The Harmonic Balance method provides a heuristic approach for finding
truncated Fourier series as an approximation to the periodic solutions of
ordinary differential equations. Another natural way for obtaining these type
of approximations consists in applying numerical methods. In this paper we
recover the pioneering results of Stokes and Urabe that provide a theoretical
basis for proving that near these truncated series, whatever is the way they
have been obtained, there are actual periodic solutions of the equation. We
will restrict our attention to one-dimensional non-autonomous ordinary
differential equations and we apply the results obtained to a couple of
concrete examples coming from planar autonomous systems
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