Continuation and Collocation for Parameter-Dependent Boundary Value Problems

Abstract

The numerical approximation of boundary value problems in the context of one-parameter continuation is considered. A collocation discretization of parameter-dependent boundary value problems is suggested. The convergence properties are analysed and a stable algorithm is presented. Tangent continuation and steplength control are combined with a Gauss–Newton type corrector, which is shown to be quadratically convergent. Based on this analysis, a general purpose continuation code, COLCON, has been implemented. Numerical examples demonstrating the efficiency of the approach are presented.