Abstract: Spectrum characteristic of linear dissipative compact schemes and corresponding fully-discrete forms based on m-order Runge-Kutta algorithm are investigated by Fourier analysis.A 5-th order scheme is empolyed to study propagation of a classical high-frequency wave and eigen-value problem of a supersonic plane Couette flow as well as its boundary value stability.Numerical results demonstrate favorable spectrum characteristic of dissipative compact schemes.

Key words: high-order accurate scheme, dissipative compact scheme, Fourier analysis, group velocity, phase velocity