An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems
In a recent paper, the present authors derived an automatic continuation algorithm for the solution of linear singular perturbation problems. The algorithm was incorporated into two general-purpose codes for solving boundary value problems, and it was shown to deal effectively with a large test set of linear problems. The present paper describes how the continuation algorithm for linear problems can be extended to deal with the nonlinear case. The results of extensive numerical testing on a set of nonlinear singular perturbation problems are given, and these clearly demonstrate the efficacy of continuation for solving such problems.
automatic continuation nonlinear boundary value problems algorithms singular perturbation problem performance theory mesh selection