2019
Том 71
№ 1

All Issues

Gavrilyuk I. P.

Articles: 3
Article (Ukrainian)

FD-method for an eigenvalue problem with nonlinear potential

Gavrilyuk I. P., Klymenko A. V., Makarov V. L., Rossokhata N. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 1. - pp. 14–28

Using the functional discrete approach and Adomian polynomials, we propose a numerical algorithm for an eigenvalue problem with a potential that consists of a nonlinear autonomous part and a linear part depending on an independent variable. We prove that the rate of convergence of the algorithm is exponential and improves as the order number of an eigenvalue increases. We investigate the mutual influence of the piecewise-constant approximation of the linear part of the potential and the nonlinearity on the rate of convergence of the method. Theoretical results are confirmed by numerical data.

Article (Ukrainian)

Estimates for the convergence of the penalty method for second-order variational elliptic inequalities

Gavrilyuk I. P., Sazhenyuk V. S., Voitsekhovskii S. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 245–250

Article (Ukrainian)

Exact and truncated schemes of any order of accuracy for a class of one-dimensional variational inequalities

Gavrilyuk I. P.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 563–568