Steady state calculation of oscillators using continuation methods

Shooting, finite difference or Harmonic Balance techniques in conjunction with Newton´s method are widely employed for the numerical calculation of limit cycles of oscillators. The resulting set of nonlinear equations are normally solved by damped Newton´s method. In some cases however divergence occurs when the initial estimate of the solution is not close enough to the exact one. A two-dimensional homotopy method is presented in this paper which overcomes this problem. The resulting linear set of equations employing Newton´s method is under-determined and is solved in a least squares sense for which a rigorous mathematical basis can be derived