  We present a Rvachev function method with the Chebysev collocation for the
stability analysis of fluid flow. The strategy is to construct an approximate
solution that satisfies all boundary conditions exactly. As an example, we
consider the stability problem of the two-dimensional flow of an incompressible
viscous liquid near a circular cylinder. The results coincide well with the
reference data. The method is simpler than the widely used spectral/hp element
method, in particular because it does not require mesh generation, and the
collocation algorithm does not handle the boundary conditions or any geometric
information.
