ABSTRACT
Eigenvalue problems play an important role in theoretical and applied hydrodynamics. Such problems have some specific features which make their solution very difficult. Quite often one has to deal with generalized eigenvalue problems. In this chapter, we describe some results of numericalanalytical investigation of two meaningful problems in hydrodynamics by the method of accelerated convergence. The first is the Laplace-Hough problem which describes surface waves on a spherical layer of heavy fluid on a rotating gravitating sphere [21, 57]. The second problem is that of travelling waves in a strongly stratified heavy fluid [26].
