A numerical continuation method for parameter-dependent boundary value problems using bvpsuite 2.0

Abstract

The Matlab package bvpsuite 2.0 is a numerical collocation code for the approximation of solutions of a broad range of boundary value problems in ordinary differential equations. In this article, its newly implemented pathfollowing module with automated step-length control is presented. Two versions using the pseudo-arclength continuation method, allowing pathfollowing beyond turning points, were developed, both taking advantage of the existing features of bvpsuite 2.0 such as error estimation and mesh adaptation. The first version is based on the Gauss-Newton method. The second version is now contained in the package bvpsuite 2.0 and uses its built-in iterative method, the Fast Frozen Newton method. Their operating principles are presented and their performance is compared by means of the computation of some pathfollowing problems. Furthermore, the results of computations with bvpsuite 2.0 for a problem with path bifurcations are presented.