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Numerical implementation and numerical properties of a new matching scheme developed for stability analysis of flowing plasmas are presented. Similar with the classical asymptotic matching scheme, the new scheme divides a whole plasma region into two parts: inner layers and outer regions. Before solving the matching problem, the inner layers must be allocated, which should contain resonant surfaces. Regions except for the inner layers are called outer regions, and are governed by the Newcomb equation that is an inertia-less linearized magnetohydrodynamic equation. For flow-less plasmas, resonance occurs at the so-called rational surface; hence, one can identify the rational surface as the inner layer. However, when there exits a flow, fundamental difficulty arises. The resonance occurs somewhere in a finite region and its location is not known a priori; hence, one cannot know where to set the inner layer. The new scheme exploits the inner “region” with finite width. Then, the inner region can contain the resonant surface, even if the location of resonance cannot be prescribed. In the new scheme, singularities are contained in the inner regions, and the Newcomb equation in the outer regions becomes regular; hence, the new scheme is numerically tractable. Also, since the new scheme is based on the boundary layer theory, it can save much computation time.