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SUMMARY:Raffaele D’Ambrosio (Università dell'Aquila\, Italy)
DTSTART:20210706T140000Z
DTEND:20210706T150000Z
DTSTAMP:20260423T035411Z
UID:SNAP/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SNAP/6/">Pri
 nciples of stochastic geometric numerical integration</a>\nby Raffaele D
 ’Ambrosio (Università dell'Aquila\, Italy) as part of Seminars on Numer
 ics and Applications\n\n\nAbstract\nThis talk is devoting to sharing recen
 t advances in the numerical preservation of invariant\nlaws characterizing
  the underlying dynamics of stochastic problems\, following the spirit\nof
  the so-called stochastic geometric numerical integration. We first addres
 s stochastic\nHamiltonian problems\, in order to obtain long-term energy c
 onservation. Specifically\,\nwe study the behaviour of stochastic Runge-Ku
 tta methods arising as stochastic perturbation\nof symplectic Runge-Kutta 
 methods. The analysis is provided through epsilon-expansions\nof the solut
 ions (where epsilon is the amplitude of the stochastic fluctuation) and sh
 ows\nthe presence of secular terms destroying the long-term preservation o
 f the expected Hamiltonian.\nThen\, an energy-preserving scheme is develop
 ed and analyzed to fill this gap in.\nWe finally consider the nonlinear st
 ability properties of stochastic theta-methods with\nrespect to mean-squar
 e dissipative nonlinear test problems\, generating a mean-square\ncontract
 ive behaviour. The pursued aim is that of making the same property visible
  also along\nthe numerical discretization via stochastic theta–methods: 
 this issue is translated into\nsharp stepsize restrictions depending on so
 me parameters of the problem\, accurately estimated.\nA selection of numer
 ical tests confirming the effectiveness of the analysis and its sharpness\
 nis also provided.\n<br />\n<b>References</b>\n<br />\n[1] C. Chen\, D. Co
 hen\, R. D’Ambrosio\, A. Lang\, <i>"Drift-preserving numerical inte-grat
 ors for stochastic Hamiltonian systems"</i>\, Adv. Comput. Math. 46\, arti
 cle number 27 (2020).\n<br />\n[2] R. D’Ambrosio\, <i>"Numerical approxi
 mation of differential problems"</i>\, Springer (toappear).\n<br />\n[3] R
 . D’Ambrosio\,  S.  Di Giovacchino\, <i>"Mean-square  contractivity  of 
  stochastic theta-methods"</i>\, Comm. Nonlin. Sci. Numer. Simul. 96\, art
 icle number 105671 (2021).\n<br />\n[4] R. D’Ambrosio\,  S.  Di Giovacch
 ino\, <i>"Nonlinear  stability  issues  for  stochastic Runge-Kutta method
 s"</i>\, Comm. Nonlin. Sci. Numer. Simul. 94\, article number 105549 (2021
 ).\n<br />\n[5] R. D’Ambrosio\, G. Giordano\, B. Paternoster\, A. Ventol
 a\, <i>"Perturbative analysis of stochastic Hamiltonian problems under tim
 e discretizations"</i>\, Appl. Math. Lett. 120\, article number 107223 (20
 21).\n
LOCATION:https://researchseminars.org/talk/SNAP/6/
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