Forced‐convergence iterative schemes for the approximation of invariant manifolds

In many dynamical systems, an invariant manifold attracts the phase‐space flow. These manifolds can be approximated by an iterative method based on a functional equation treatment. However, a convergent mapping is not automatically generated from the functional equation. Nevertheless, it is possible to construct a convergent mapping by a simple modification of the original functional equation. As an example, a convergent sequence of approximations to the slow manifold of the Michaelis–Menten system is constructed.

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