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...

In this paper, we present a numerical approach to solving singularly perturbed semilinear convection-diffusion problems. The nonlinear part of the problem is linearized via quasilinearization technique. We then design and implement fitted operator finite difference method solve sequence linear problems that emerges from process. carry out rigorous analysis attest convergence proposed procedure ...

Pointwise accurate numerical methods are constructed and analysed for three classes of singularly perturbed first order transport problems. The involve piecewise-uniform Shishkin meshes the approximations shown to be parameter-uniformly convergent in maximum norm. A problem from modelling fluid–particle interaction is formulated used as a test these methods. Numerical results presented illustra...