Abstract: This paper is a continuation of the domain decomposition method according to thephysics scale proposed in [1] and [2]. Starting from systems of ordinary differentialequattons, a solution is decomposed into an outer solution (0) and its boundary layercorrections (BLC) mainly on the fixed boundary. For efficient numerical solution,different equations, different numerical methods and different grids can be suitablychosen for the different scales. This paper also gives the characteristic nature and well-posed boundary condition about artificial compressible equations. Numericalexperiments show that the computational method and the couple process presented inthe paper are effective.

Key words: zone decompose, singular perturbation, artificial compress