Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+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 theQ-quadratically convergent method.
['Gerd Pönisch']
I am writing a research paper on a idea Computing hysteresis points of nonlinear equations depending on two parameters
[{"from": "human", "value": "I am writing a research paper on a idea Computing hysteresis points of nonlinear equations depending on two parameters"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+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 theQ-quadratically convergent method."}]