Computing simple bifurcation points using a minimally extended system of nonlinear equations (Q1060814)

The present paper deals with the computation of simple bifurcation points of nonlinear parameterdependent equations. At first, a minimally extended system of nonlinear equations is constructed by addition of one parameter and two equations. This augmented system has an isolated solution which yields to the simple bifurcation point directly. Using the structural properties of this auxiliary system an adapted Newton-like method is developed not requiring evaluations of second derivatives. Finally, the results of some computer experiments show the efficiency of the R- quadratically convergent method.