Localized Basis Function Method for Computing Limit Cycle Oscillations

An alternate approach to the standard harmonic balance method (based on Fourier transforms) is proposed. The proposed method begins with an idea similar to the harmonic balance method, i.e. to transform the initial set of differential equations of the dynamics to a set of discrete algebraic equations. However, as distinct from previous harmonic balance techniques, the proposed method uses a set of basis functions which are localized in time and are not necessarily sinusoidal. Also as distinct from previous harmonic balance methods, the algebraic equations obtained after the transformation of the differential equations of the dynamics are solved in the time domain rather than the frequency domain. Numerical examples are provided to demonstrate the performance of the method for autonomous and forced dynamics of a Van der Pol oscillator.