The paper is focused on analyzing the conservation issues of stochastic-methods when applied to nonlinear damped stochastic oscillators. In particular, we are interested in reproducing the long-term properties of the continuous problem over its discretization through stochastic-methods, by preserving the correlation matrix. This evidence is equivalent to accurately maintaining the stationary density of the position and the velocity of a particle driven by a nonlinear deterministic forcing term and an additive noise as a stochastic forcing term. The provided analysis relies on a linearization of the nonlinear problem, whose effectiveness is proved theoretically and numerically confirmed.

On the numerical structure preservation of nonlinear damped stochastic oscillators

D'Ambrosio R.;Scalone C.
2020-01-01

Abstract

The paper is focused on analyzing the conservation issues of stochastic-methods when applied to nonlinear damped stochastic oscillators. In particular, we are interested in reproducing the long-term properties of the continuous problem over its discretization through stochastic-methods, by preserving the correlation matrix. This evidence is equivalent to accurately maintaining the stationary density of the position and the velocity of a particle driven by a nonlinear deterministic forcing term and an additive noise as a stochastic forcing term. The provided analysis relies on a linearization of the nonlinear problem, whose effectiveness is proved theoretically and numerically confirmed.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/150144
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