Mentynskyi S. M.
Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 284–288
We propose a general scheme for the two-sided approximation of solutions of boundary-value problems for ordinary differential equations. This scheme involves a number of known and new two-sided methods. In our investigation, we use constructions of the Samoilenko numerical-analytic method together with the procedure of the construction of two-sided methods proposed by Kurpel’ and Shuvar.
Two-Sided Approximation of Solutions of a Multipoint Problem for an Ordinary Differential Equation with Parameters
Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 125–130
We construct an algorithm for the two-sided approximation of a solution of a multipoint boundary-value problem for a quasilinear differential equation under assumptions that are two-sided analogs of the Pokornyi B-monotonicity of the right-hand side of the equation. We establish conditions for the monotonicity of successive approximations and their uniform convergence to a solution of the problem.