The Calculation of Turning Points of Nonlinear Equations

Abstract

This paper is concerned with the determination of a type of singular point, called a “turning” or “limit” point, of nonlinear equations depending on a parameter. An enlarged system is introduced for which the turning point is a nonsingular solution and thus standard methods can be used to compute it. An efficient implementation of Newton’s method in the finite-dimensional case is presented and numerical results for discretizations of a differential equation and an integral equation are given.