New general solutions of ordinary differential equations are introduced and their properties are established. We develop new methods for the solution of boundary-value problems based on the construction and solution of the systems of algebraic equations for arbitrary vectors of the general solutions. An approach to finding the initial approximation to the required solution of a nonlinear boundary-value problem is proposed.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 7, pp. 884–905, July, 2019.
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Dzhumabaev, D.S. New General Solutions of Ordinary Differential Equations and The Methods for The Solution of Boundary-Value Problems. Ukr Math J 71, 1006–1031 (2019). https://doi.org/10.1007/s11253-019-01694-9
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DOI: https://doi.org/10.1007/s11253-019-01694-9