Multiparameter parallel search branch switching

Abstract

A continuation method (sometimes called path following) is a way to compute solution curves of a nonlinear system of equations with a parameter. We derive & simple algorithm for branch switching at bifurcation points for multiple parameter continuation, where surfaces bifurcate along singular curves on a surface. It is a generalization of the parallel search technique used in the continuation code AUTO, and avoids the need for second derivatives and a full analysis of the bifurcation point. The one parameter case is special. While the generalization is not difficult, it is nontrivial, and the geometric interpretation may be of some interest. An additional tangent calculation at a point near the singular point is used to estimate the tangent to the singular set. © World Scientific Publishing Company.