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A numerical scheme has been devised to calculate discrete spiral modes in a fluid-dynamical model of disk galaxies. The procedure is free from the usual restrictions imposed upon the asymptotic theory. A radiation condition has been formulated as one of the boundary conditions. For a test model galaxy with moderately low surface density, quantitative agreement is found between the asymptotic spiral modes and the corresponding ones obtained from the present scheme. The present scheme should find ready application to the study of open spiral modes.

Unstable spiral modes in disk-shaped galaxies: A general fluid dynamical theory with some preliminary results