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 al gorithm for the solution of linear singular perturbation problems. The algo rithm 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 algori thm for linear problems can be extended to deal with the nonlinear case. Th e results of extensive numerical testing on a set of nonlinear singular per turbation problems are given, and these clearly demonstrate the efficacy of continuation for solving such problems.