Symplectic Integration of Hamiltonian Systems with Additive Noise

@article{Milstein2002SymplecticIO,
  title={Symplectic Integration of Hamiltonian Systems with Additive Noise},
  author={G. N. Milstein and Yu. M. Repin and Michael V. Tretyakov},
  journal={SIAM J. Numerical Analysis},
  year={2002},
  volume={39},
  pages={2066-2088}
}
Hamiltonian systems with additive noise possess the property of preserving symplectic structure. Numerical methods with the same property are constructed for such systems. Special attention is paid to systems with separable Hamiltonians and to second-order differential equations with additive noise. Some numerical tests are presented. 

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References

Publications referenced by this paper.
Showing 1-10 of 19 references

Suris, Hamiltonian methods of Runge-Kutta type and their variational interpretation

  • B. Yu
  • Math. Model.,
  • 1990
Highly Influential
10 Excerpts

On the canonicity of mappings that can be generated by methods of Runge-Kutta type for integrating systems ẍ = −∂U/∂x, U.S.S.R

  • Yu. B. Suris
  • Comput. Math. and Math. Phys.,
  • 1989
Highly Influential
4 Excerpts

Mécanique Aléatoire

  • J.-M. Bismut
  • Lecture Notes in Math. 866, Springer, Berlin
  • 1981
Highly Influential
4 Excerpts

Yu

  • G. N. Milstein
  • M. Repin, and M.V. Tretyakov, Symplectic Methods…
  • 2001
5 Excerpts

Tret’yakov, Mean-square numerical methods for stochastic differential equations with small noises

  • M.V.G.N. Milstein
  • SIAM J. Sci. Comput.,
  • 1997
1 Excerpt

On the canonicity of mappings that can be generated by methods of Runge - Kutta type for integrating systems ẍ

  • Yu. B. Suris
  • Comput . Math . and Math . Phys .
  • 1994

Simulation of one-dimensional noisy Hamiltonian systems and their application to particle storage rings

  • M. Seeßelberg, H. P. Breuer, H. Mais, F. Petruccione, J. Honerkamp
  • Z. Phys. C, 62
  • 1994
1 Excerpt

Tret’jakov, Numerical integration of Hamiltonian systems with external noise

  • S.V.M.V. Tretyakov
  • Phys. Lett. A,
  • 1994
1 Excerpt

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