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This paper presents an alternative approach for the computation of trajectorysegments on slow manifolds of saddle type. This approach is based on iterativemethods rather than collocation-type methods. Compared to collocation methods,that require mesh refinements to ensure uniform convergence with respect to$\epsilon$, appropriate estimates are directly attainable using the method ofthis paper. The method is applied to several examples including: A model for apair of neurons coupled by reciprocal inhibition with two slow and two fastvariables and to the computation of homoclinic connections in theFitzHugh-Nagumo system.

Computation of saddle type slow manifolds using iterative methods