A numerical approach to proof in the problem of the stability of plane Poiseuille flow

In the theory describing hydrodynamic stability and the evolution of supercritical flows, there are many problems that cannot be solved by means of the existing analytical methods. In such cases, machine computations can sometimes be used to prove a particular hypothesis. The numerical approach to proof is demonstrated here for the Orr-Sommerfeld spectral problem. In accordance with this approach, an a priori investigation is first made of the smoothness of the solution and its singularities, if any. An efficient algorithm is then constructed, and, finally, machine computations are carried out to obtain the required analytical result.