The initial-boundary value problems of the Navier-Stokes equations are solved by means of a fractional step approach. The equations are split into Euler equations with no diffusion term and diffusion equations with no convection term within each time step, and then the convergence of the approximate solutions is proved. Unlike the conventional approach, we apply nonhomogeneous diffusion equations instead of homogeneous ones. This paper, where linearized equations are considered, is the first one of a series of papers.
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