Effective solution of hydrodynamic stability problems, as well as solution of the eigenvalue problem for non-selfadjoint operators in general cases can be obtained only numerically. However, in this case standard numerical methods are usually not applicable: the eigenfunctions of linear stability problem have poor properties. Thus, the differential sweep method is applied for solving this eigenvalue problem. This step reduces the problem to a sequence of Cauchy problems for nonlinear ordinary differential equations system which can be easily integrated numerically. At the same time, an iterative process for eigenvalues is carried out. It is found out that increasing of Prandtl number leads to stabilization of the flow with respect to small perturbations.