We focus on the study of stochastic Hamiltonian problem driven by additive noise. Stochastic Runge-Kutta methods 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
Giordano Giuseppe;Paternoster beatrice
2022-01-01
Abstract
We focus on the study of stochastic Hamiltonian problem driven by additive noise. Stochastic Runge-Kutta methods 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.File in questo prodotto:
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