We focus on the study of stochastic Hamiltonian problem driven by additive noise. Stochastic Runge-Kutta methods [3, 4] obtained as stochastic perturbation of symplectic Runge-Kutta methods exhibit a remarkable error growth as the parameter ε of the diffusive part increases. Through a perturbative theory, we investigate the reason of this behaviour, due to the presence of a secular term ε √t destroying the overall conservation accuracy.

Numerical Conservation Issues for Stochastic Hamiltonian Problems

D'Ambrosio R.;
2022

Abstract

We focus on the study of stochastic Hamiltonian problem driven by additive noise. Stochastic Runge-Kutta methods [3, 4] obtained as stochastic perturbation of symplectic Runge-Kutta methods exhibit a remarkable error growth as the parameter ε of the diffusive part increases. Through a perturbative theory, we investigate the reason of this behaviour, due to the presence of a secular term ε √t destroying the overall conservation accuracy.
978-0-7354-4182-8
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/186872
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