An Analytical Approach to the Determination of Neutral Stability Curves

Abstract

A powerful analytical method — introduced by Lanczos [1] — is applied for the calculation of neutral stability curves of hydrodynamic stability problems. This method based on a special quadrature formula is applicable to all kind of two-point-boundary value problems for ordinary differential equations defined on an interval of finite length. Compared with other purely numerical methods for which large systems of ordinary differential equations must be solved by the use of a large computer with a big amount of computing time [2] this method needs only a smallscale computer and has the advantage of leading to an explicit analytical formula for the neutral stability curves. Using this kind of approach the tremendous amount of computing time is avoided and the dependence of the neutral stability curves on other eigenvalue parameters can be studied analytically.