For a second-order quasilinear singularly perturbed problem under the Dirichlet boundary conditions, we propose new asymptotic numerical method, which involves two problems: reduced with one-side condition and novel layer correction two-sided condition. Through introduction of variables, both problems are transformed to set three first-order initial value zero conditions. The Runge–Kutta method...

The first aim of this article is to present the link between turnpike property and singular perturbations theory: one being a particular case second one. Then, thanks link, we set up new framework based on continuation methods for resolution singularly perturbed optimal control problems. We consider case, then, generalize approach general problems with (that fast but also slow variables). illus...