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An efficient numerical method for the linear stability equations of a spatially periodic channel flow is presented. The method is based on global Fourier-Chebyshev approximation of a disturbance velocity field. The physical flow domain is embedded in a larger computational domain and the boundary conditions are re-formulated as internal conditions imposed at immersed boundaries. The advantage of this approach is an avoidance of domain mapping, leading to tremendous complication of governing equations and to excessive computational cost. The results of numerical tests are presented. Favorable convergence properties with respect to the length of the Fourier expansions are demonstrated.