COMPUTING HYSTERESIS POINTS OF NONLINEAR EQUATIONS DEPENDING ON TWO PARAMETERS.

A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system of n nonlinear equations in n variables depending on two parameters. By addition of two equations a minimally extended system of n plus 2 nonlinear equations is constructed for which the hysteresis point is an isolated solution. An efficient implementation of Newton's method is presented not requiring evaluations of second derivatives of the original problem. Two numerical examples show the efficiency of the Q-quadratically convergent method.