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Dissipation of mean energy of discretized linear oscillators under random perturbations. (English) Zbl 1144.65300

Summary: This paper deals with the problem of correct asymptotic dissipation of mean energy functional related to numerical integration of systems of uncoupled linear oscillators under random perturbations. It is shown that the drift-implicit trapezoidal method provides numerical approximations which possess the correct asymptotic behavior of their mean energy functional compared to that of the underlying exact solution as integration time \(t\) advances to infinity.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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