Abstract
Singularities of application of the method of functional expansions in singular problems of oscillation theory are considered, where conditions of boundedness of a solution play the role of boundary conditions. A description is given of a method of numerical realization of a convergence condition of the corresponding functional series. A problem of oscillations of a string that freely hangs in the gravitational field is considered (the expansion of a solution into a power series is used), the problem of oscillations of a flag in a flow of fluid (expansions in half-integer powers of coordinates), and the problem on the construction of periodic solutions of the Mat've equation (expansion into a trigonometric series).
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References
É. Kamke, Manual in Ordinary Differential Equations [in Russian], Nauka, Moscow (1976).
M. Abramovich and I. Stigan, Manual for Special Functions [in Russian], Nauka, Moscow (1979).
G. Shlikhting, Theory of a Boundary Layer [in Russian], Nauka, Moscow (1973).
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Translated from Dinamicheskie Sistemy, No. 7, pp. 123–132, 1988.
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Temnenko, V.A. A numerical-analytic method of solution of some singular problems of oscillation theory. J Math Sci 65, 1585–1591 (1993). https://doi.org/10.1007/BF01097669
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DOI: https://doi.org/10.1007/BF01097669