Large sparse continuation problems

摘要

We study and develop efficient and versatile Predictor—Corrector continuation methods for large sparse problems. The first object is to show how special solving methods for a large sparse linear systems can be incorporated into the basic steps of a continuation method. Next we describe how to use a special nonlinear conjugate gradient method to perform the corrector phase. It is shown how such methods can be used to detect bifurcation points, and how to trace bifurcating solution branches by using local perturbations. Finally, a numerical example involving bifurcating branches of a nonlinear eigenvalue problem is given.