Computing hysteresis points of nonlinear equations depending on two parameters
type: Item
instance of: scholarly article
title: Computing hysteresis points of nonlinear equations depending on two parameters
zbMATH Open document ID: 0613.65053
DOI: 10.1007/BF02307709
published in: Computing
publication date: 1987-01-01T00:00:00Z
review text: 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 \(n+2\) 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.
Mathematics Subject Classification ID: 65B15
zbMATH DE Number: 3992812
zbMATH Keywords: direct method
zbMATH Keywords: hysteresis point
zbMATH Keywords: double turning point
zbMATH Keywords: cusp point
zbMATH Keywords: numerical examples
zbMATH Keywords: inexact Newton method
zbMATH Keywords: local convergence
author: G. Pönisch
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02307709
OpenAlex ID: W2280989090
description: scientific article; zbMATH DE number 3992812