Transformations reducing the order of the parameter in differential eigenvalue problems (Q1108747)

A family of order-reducing transformations applicable to a wide class of differential eigenvalue problems with nonlinear parameter dependence is developed.The highest or the first few highest powers of the parameter are removed, leading to the increased efficiency of the global numerical eigenvalue search scheme of choice. The technique of choice in this paper is one due to \textit{T. J. Bridges} and \textit{P. J. Morris} [ibid. 55, 437- 460 (1984; Zbl 0543.65063)]. In bounded domains, it consists of representing the eigenfunction in terms of a truncated Chebyshev series and determining the eigenvalues from the linear algebraic problem governing the coefficients of the Chebyshev polynomials. For unbounded domain problems the cost reduction is accompanied by an increased accuracy and increased searching capability of the spectral technique. Applications to the spatial stability of the Orr-Sommerfeld problems for channel, boundary-layer, and wake flows are demonstrated.