2019
Том 71
№ 11

All Issues

Mentynskyi S. M.

Articles: 2
Brief Communications (Ukrainian)

Two-Sided Approximation of Solutions of Boundary-Value Problems

Mentynskyi S. M., Shuvar B. A.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

Two-Sided Approximation of Solutions of a Multipoint Problem for an Ordinary Differential Equation with Parameters

Mentynskyi S. M.

↓ Abstract   |   Full text (.pdf)

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.