Mathematical modeling the values of eigenfunctions finding for Orr-Sommerfeld’s problem of hydrodynamical stability theory via the method of regularized traces

In this paper the mathematical model of computing the values of the eigenfunctions of the Orr-Sommerfeld’s operator. Using the method of regularized traces, we obtain simple formulas to find the values of the first eigenfunctions of the perturbed self-adjoint operators. The algorithms make it possible to calculate the values of the eigenfunction of the perturbed operators matter known to the previous values of their eigenfunctions or not. We obtain estimates of residual sums of functional series “weighted” perturbation theory corrections discrete operators, and prove their convergence. For the numerical implementation of the method found effective algorithms for finding “weighted” perturbation theory corrections, which can be approximated using the sum of series of functions of Rayleigh-Schrodinger right amount of members. The numerical experiments computing the values of eigenfunctions of hydrodynamic stability theory show that the method is consistent with other known methods (A.N. Krylov and A.M. Danilevsky). The method of regularized traces showed its reliability and high efficiency.