Multiparameter Parallel Search Branch Switching

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 a simple algorithm for
branch switching at bifurcation points for multiple parameter continuation, where surfaces bifurcate
along a 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 non-trivial, 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.

By: Michael E. Henderson

Published in: RC23150 in 2004


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