Following paths through turning points

Abstract

Abstract.The use of the continuation principle in the solution of systems of nonlinear equations frequently leads to the need to follow trajectories through turning points. This can be done by using a different parametrization at every step along the trajectory. We show how to construct accurate predictors and adaptive steplength estimators for use in predictor-corrector algorithms which follow trajectories in this way.

Continuation and Local Perturbation for Multiple Bifurcations

“…Predictor-corrector type continuation method. Let Yi (xi, Ai) N+I be a point which has been accepted as an approximating point for c. A new point zi+l,1 is predicted either by interpolation [29] or an Adams-Bashforth predictor [6], [12]. The Euler predictor [2], [4] (2.4) z+l,1 Yi A-t u Downloaded 12/29/12 to 152.3.102.242.…”