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On a simulation of the oscillation excited by a random force. (English) Zbl 0597.65067
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
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)
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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.
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