Method of polynomial approximations for the investigation of boundary value problems (Q1063402)

We suggest a polynomial modification of the numerical-analytic method, developed by \textit{A. M. Samojlenko} and \textit{V. A. Ronto} [ibid. 33, 467- 475 (1981; Zbl 0479.65046)], for the investigation of solutions of two- point boundary-value problems for a selected class of ordinary differential equations. The distinguishing feature of the method of polynomial approximations consists in that the higher approximations to the solutions of the considered boundary value problems as well as to the defining equations whose fixed points give the initial values of the desired solutions are constructed easily by its scheme. In addition, the sequence of approximate solutions can be analytically represented as algebraic polynomials that satisfy given boundary conditions.