New general solutions of ordinary differential equations and the methods of solving the boundary-value problems - Dzhumabaev, D. S.; Джумабаев, Д. С.; Джумабаев, Д. С. (Institute of Mathematics, NAS of Ukraine, 2019)
UDC 517.624 New general solutions of ordinary differential equations are introduced and their properties are established. We develop new methods of solving the boundary-value problems based on the construction and solving of the systems of algebraic equations for arbitrary vectors of the general solutions. An approach to finding the initial approximation to the solution of a nonlinear boundary-value problem is proposed.