Holický, Petr On a simulation of the oscillation excited by a random force. (English) Zbl 0597.65067 Kybernetika 22, 176-188 (1986). A simulation method is presented for approximating the solution of a system of stochastic ordinary differential equations. The method is applied to an example representing the oscillation of a two mass mechanical system subject to random excitation. Numerical results are compared to those obtained by Dimentburg for the same example. Reviewer: M.D.Lax MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 65C99 Probabilistic methods, stochastic differential equations 70L05 Random vibrations in mechanics of particles and systems 34F05 Ordinary differential equations and systems with randomness 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:system of stochastic ordinary differential equations; oscillation of a two mass mechanical system; random excitation; Numerical results × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] M. F. Dimentberg: Nelineynye stokhasticheskiye zadachi mekhanicheskikh kolebaniy. Nauka, Moskva 1980, 143-147. [2] W. Rumelin: Numerical Treatment of Stochastic Differential Equations. Report Nr. 12, Universitát Bremen 1980. [3] J. M. C. Clark, P. J. Cameron: The maximum rate of convergence of discrete approximations for stochastic differential equations. Stochastic Differential System - Filtering and Control (B. Grigelionis. (Lecture Notes on Control and Information Sciences 25.) Springer-Verlag, Berlin-Heidelberg-New York 1980, 162-171. [4] A. Yu. Veretennikov: O stokhasticheskikh uravneniyakh s vyrozhdennoy po chasti peremennykh diffuziyey. Izv. Akad. Nauk SSSR Ser. Mat. 47 (1983), 1, 189-196. [5] M. Nisio: On the existence of solution of stochastic differential equations. Osaka J. Math. 70 (1973), 185-208. · Zbl 0268.60057 [6] N. V. Krylov: Upravlyayemye processy diffuziyonnovo tipa. Nauka, Moskva 1977. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.