2019
Том 71
№ 11

All Issues

Kolomiets O. V.

Articles: 2
Brief Communications (Ukrainian)

On the Application of the Averaging Principle in Stochastic Differential Equations of Hyperbolic Type

Kolomiets O. V., Kolomiyets V. G., Mitropolskiy Yu. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 711-715

We prove a theorem on the application of the Bogolyubov–Mitropol'skii averaging principle to stochastic partial differential equations of the hyperbolic type.

Brief Communications (Ukrainian)

On the application of numerical methods to the solution of nonlinear second-order differential equations with random deviations of argument

Kolomiets O. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 10. - pp. 1433–1441

We consider the application of the Krylov-Bogolyubov-Mitropol’skii asymptotic method and Runge-Kutta methods to the investigation of oscillating solutions of quasilinear second-order differential equations with random deviations of argument. For specific equations, we obtain approximate numerical solutions and characteristics of random oscillations.