Quasisymplectic integrators for stochastic differential equations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 69, Issue 4 1, 2004, Pages

  Mannella, R ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DAMPING; EQUATIONS OF MOTION; GAUSSIAN NOISE (ELECTRONIC); MONTE CARLO METHODS; OSCILLATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DISTRIBUTIONS;

FOKKER-PLANCK EQUATION; KRAMERS-MOYAL EXPANSION; OSCILLATION FREQUENCY; SYMPLECTIC STOCHASTIC DYNAMICS;

BROWNIAN MOVEMENT;

EID: 42749103458     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. For a classical introduction, see Noise in Nonlinear Dynamical Systems, edited by F. Moss and P. V. E. McClintock (Cambridge University Press, Cambridge, 1989), Vol. 1-3.
2. P. E. Kloeden and E. Platen, Numerical Simulation of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992).
3. J. Garcia-Ojalvo and J. Sancho, Noise in Spatially Extended Systems (Springer-Verlag, Berlin, 1999).
4. G. N. Milstein and M. V. Tret'yakov, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 34, 2142 (1997).
5. R. Mannella, Int. J. Mod. Phys. C 13, 1177 (2002).
6. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 2001).
7. A. C. Brańka and D. M. Heyes, Phys. Rev. E 60, 2381 (1999).
8. H. A. Forbert and S. A. Chin, Phys. Rev. E 63, 016703 (2000).
9. Ji Qiang and S. Habib, Phys. Rev. E 62, 7430 (2000).
10. W. Paul and D. Y. Yoon, Phys. Rev. E 52, 2076 (1995).
11. J. A. Izaguirre, D. P. Catarello, J. M. Wozniak, and R. D. Skeel, J. Chem. Phys. 114, 2090 (2001).
12. R. D. Skeel and J. A. Izaguirre, Mol. Phys. 100, 3885 (2002).
13. W. Wang and R. D. Skeel, Mol. Phys. 101, 2149 (2003).
14. G. N. Milnstein and M. V. Tretyakov, Numerical Methods for Langevin Type Equations Based on Symplectic Integrators (Weierstrab-Institut für Angewandte Analysis und Stochastik, Berlin, 2002).
15. G. N. Milnstein, Yu. M. Repin, and M. V. Tretyakov, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 40, 1583 (2003).
16. G. N. Milnstein and M. V. Tretyakov, IMA J. Numer. Anal. 23, 1 (2003).
17. M. Freidlin and A. D. Wentzel, Random Perturbations in Dynamical Systems (Springer, New York, 1984).
18. G. G. Batrouni, G. R. Katz, A. S. Kronfeld, G. P. Lepage, B. Svetitsky, and K. G. Wilson, Phys. Rev. D 32, 2736 (1985).
19. H. Yoshida, Phys. Lett. A 150, 262 (1990).
20. J. M. Sanz-Serna, Acta Numerica 1, 243 (1991).
21. R. Mannella, in Supercomputation in Nonlinear and Disordered Systems, edited by L. Vasquez, F. Tirado, and I. Martin (World Scientific, Singapore, 1997), pp. 100-129.
22. C. M. Luscher, Comput. Phys. Commun. 79, 100 (1994).
23. F. James, Comput. Phys. Commun. 79, 111 (1994).
24. G. Marsaglia and W. W. Tsang, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 5, 349 (1984).