Numerical simulations: boundary feedback stabilization

Numerical simulation of boundary feedback laws for stabilization of parabolic systems is described. The numerical method proposed by J. Lund et al. (1991) addressed the use of the fully Sinc-Galerkin method for the simulation of a boundary feedback law for the classical diffusion equation. The authors complement the results of that work through the discussion and implementation of this fully Sinc-Galerkin scheme for nonlinear problems. In particular, with the simulation of the boundary feedback law introduced by C.I. Byrnes and D.S. Gilliam (1991) in mind, they focus on the numerical tracking of the (possibly slowly evolving) steady state of the system. This ability to track steady states is illustrated by an example. It forms another step torwards the simulation corresponding to the stabilization effected via the introduction of a small gain parameter