Kolomiets O. V.
On the Application of the Averaging Principle in Stochastic Differential Equations of Hyperbolic Type
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.
On the application of numerical methods to the solution of nonlinear second-order differential equations with random deviations of argument
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.