In this work, we present a method for analyzing and computing the rates of change of eigenvalues with respect A method for analysis and computation of derivatives and extremum points of variable-coefficients differential eigenvalue probto differential-eigenvalue-problem parameters as well as lems is presented. The method utilizes the orthogonality of the computing the extremum points of differential eigenvalue adjoint eigenfunctions to the homogenous part of the once or more problems. The method is applied to problems from hydrodifferentiated problem to derive an analytical expression for the dynamic stability of boundary layers. Efficient computation rate of change of eigenvalue with respect to a free parameter. The extremum point can be analyzed and computed by setting and of the rates of change of some quantity with respect to driving, respectively, the first rate of change of the eigenvalue with parameters is essential in sensitivity analysis and optimizarespect to the free parameters to zero. Higher order derivatives can tion studies. While the rates of change of a quantity with be computed by solving, sequentially, sets of inhomogeneous tworespect to a parameter can be computed using two-point point boundary value problems. The method is applied to analyze finite differences, this method has a low order of accuracy.
and compute the most amplified inviscid instability wave in twodimensional compressible boundary layers and the most amplified Moreover, higher-order-finite-difference approximations viscous instability wave in three-dimensional incompressible are costly for practical problems both in terms of computer boundary layers. It is shown analytically that while the most-ampliand user's time.
fied spatial instability wave in two-dimensional incompressible
In hydrodynamic stability, it is known that the most boundary layer is two dimensional, the corresponding most amplified wave in three-dimensional boundary layer is generally oblique.
amplified temporal instability wave in two-dimensional in-
It is also shown analytically that the most-amplified disturbance in compressible boundary layers is two dimensional. On the three-dimensional boundary layer is generally a traveling disturother hand, the most amplified waves in three-dimensional bance. Furthermore, it is shown analytically that the inviscid growth boundary layers are oblique. Furthermore, the extensive rate is an extremum point.