Note on the Two-Point Boundary Value Numerical Solution of the Orr-Sommerfeld Stability Equation

摘要

The numerical results we presented in this paper are concerned with the computation of the transition curve of the Orr-Sommerfeld stability equation. However, we have obtained results, regarding the computation of the complex or real speed λ, that were in agreement with the previous results. The procedure used to compute the eigenvalues and the eigen-functions is based upon expressing the Orr-Sommerfeld equation as a two-point boundary value system. The eigenvalues were computed one at a time, jointly with the eigenfunctions, using successive continuation on the code PASVA 3. We think that our procedure is simple, direct, and very efficient and that it can be used with relative ease on a computer.