Abstract
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 (taken to be spectral in this work). For unbounded-domain problems this 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 addressed explicitly.
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