An algorithm for the local exhaustive search for alternatives in an essentially non-linear eigenvalue problem

An algorithm for the local exhaustive search for alternatives, which enable one to reduce the number of auxiliary linear eigenvalue problems that must be solved is illustrated using the example of the problem of the supercritical behaviour of a longitudinally compressed rod at the interface of two dissimilar Winkler media. The basic principle of the algorithm consists of developing a qualitatively adequate natural form based on a complete exhaustive search for alternatives on a “widely spaced” grid with further subsequent doubling of the number of its nodes and exhaustively searching for alternatives only in the region of the roots of the natural form.