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 types 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 obtained results to a concrete example coming from a rigid cubic system. © 2012 Elsevier Inc.
|Journal||Journal of Differential Equations|
|Publication status||Published - 1 Jan 2013|
- Fixed point theorem
- Fourier series
- Harmonic Balance Method
- Hyperbolic limit cycle
- Planar polynomial system