Abstract: In this paper, we consider a self adjoint elliptic first boundary vdlue problem with a small parameter affecting the highest derivative.In the paper, we set up a new scheme by the asymptotic analysis method, compare asymptotic behavior between the solution of the difference equation and the solution of the differential equation, and show uniform convergence of the new scheme.

Key words: hybrid dynamic system, switched linear system, time-delay, controllability, controllable set, switching sequence, switching path