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Ukrainian Mathematical Journal

, Volume 51, Issue 10, pp 1617–1626 | Cite as

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

  • O. V. Kolomiets
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Abstract

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.

Keywords

Stochastic Differential Equation Time Segment Random Deviation Random Delay Random Oscillation 
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References

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    V. G. Kolomiets and O. V. Kolomiets, “On the study of oscillations in nonlinear second-order systems with random deviation of argument,” inIntegral Transformations and Their Application to Boundary-Value Problems. Collection of Scientific Papers [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1995), pp. 90–96.Google Scholar
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    N. N. Bogolyubov and Yu. A. Mitropol’skii,Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).MATHGoogle Scholar
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    V. G. Kolomiets and D. G. Korenevskii, “On the excitation of oscillations in nonlinear systems with random delay,”Ukr. Mat. Zh.,18, No. 3, 51–57 (1966).MATHCrossRefGoogle Scholar
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    D. G. Korenevskii and V. G. Kolomiets, “Some problems of the theory of nonlinear oscillations of quasilinear systems with random delays,”Mat. Fiz., Issue 3, 91–113 (1967).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • O. V. Kolomiets

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