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Volumn 18, Issue 1, 1997, Pages 203-222

A family of symplectic integrators: Stability, accuracy, and molecular dynamics applications

Author keywords

Cowell; Implicit midpoint; Leapfrog; Method of modified equations; Molecular dynamics; Numerov; St rmer; Symplectic integrator; Trapezoid; Verlet

Indexed keywords

COWELL-NUMEROV METHOD; IMPLICIT MIDPOINT METHOD; LEAPFROG METHOD; METHOD OF MODIFIED EQUATIONS; STORMER-VERLET METHOD; SYMPLECTIC INTEGRATORS; TRAPEZOID METHOD;

EID: 0030621830     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595282350     Document Type: Article
Times cited : (89)

References (34)
  • 2
    • 0001724114 scopus 로고
    • Symplectic integrators for long-term integrations in celestial mechanics
    • B. GLADMAN, M. DUNCAN, AND J. CANDY, Symplectic integrators for long-term integrations in celestial mechanics, Celestial Mech. Dynam. Astronom., 52 (1991), pp. 221-240.
    • (1991) Celestial Mech. Dynam. Astronom. , vol.52 , pp. 221-240
    • Gladman, B.1    Duncan, M.2    Candy, J.3
  • 3
    • 0040037019 scopus 로고
    • Some properties of methods for the numerical integration of systems of the form ẍ = f(x)
    • in Russian
    • Y. B. SURIS, Some properties of methods for the numerical integration of systems of the form ẍ = f(x), Zh. Vychisl. Mat. i Mat. Fiz., 27 (1987), pp. 1504-1515 (in Russian); U.S.S.R. Comput. Math. Phys., 27 (1987), pp. 149-156.
    • (1987) Zh. Vychisl. Mat. i Mat. Fiz. , vol.27 , pp. 1504-1515
    • Suris, Y.B.1
  • 4
    • 6144267603 scopus 로고
    • Y. B. SURIS, Some properties of methods for the numerical integration of systems of the form ẍ = f(x), Zh. Vychisl. Mat. i Mat. Fiz., 27 (1987), pp. 1504-1515 (in Russian); U.S.S.R. Comput. Math. Phys., 27 (1987), pp. 149-156.
    • (1987) U.S.S.R. Comput. Math. Phys. , vol.27 , pp. 149-156
  • 5
    • 36449000762 scopus 로고
    • Comment on: Reversible multiple time scale molecular dynamics
    • S. TOXVAERD, Comment on: Reversible multiple time scale molecular dynamics, J. Chem. Phys., 99 (1993), p. 2277.
    • (1993) J. Chem. Phys. , vol.99 , pp. 2277
    • Toxvaerd, S.1
  • 6
    • 0000940605 scopus 로고
    • Reply to comment on: Reversible multiple time scale molecular dynamics
    • M. TUCKERMAN, B. J. BERNE, AND G. J. MARTYNA, Reply to comment on: Reversible multiple time scale molecular dynamics, J. Chem. Phys., 99 (1993), pp. 2278-2279.
    • (1993) J. Chem. Phys. , vol.99 , pp. 2278-2279
    • Tuckerman, M.1    Berne, B.J.2    Martyna, G.J.3
  • 7
    • 0012579993 scopus 로고
    • Implicit discretization schemes for Langevin dynamics
    • G. ZHANG AND T. SCHLICK, Implicit discretization schemes for Langevin dynamics, Molecular Phys., 84 (1995), pp. 1077-1098.
    • (1995) Molecular Phys. , vol.84 , pp. 1077-1098
    • Zhang, G.1    Schlick, T.2
  • 8
    • 0003019535 scopus 로고
    • The effective order of Runge-Kutta methods
    • Conference on the Numerical Solution of Differential Equations, A. Dold, Z. Heidelberg, and B. Eckmann, eds., Springer-Verlag, New York
    • J. C. BUTCHER, The effective order of Runge-Kutta methods, in Conference on the Numerical Solution of Differential Equations, Lecture Notes in Mathematics, Vol. 109, A. Dold, Z. Heidelberg, and B. Eckmann, eds., Springer-Verlag, New York, 1969, pp. 133-139.
    • (1969) Lecture Notes in Mathematics , vol.109 , pp. 133-139
    • Butcher, J.C.1
  • 9
    • 0002613398 scopus 로고    scopus 로고
    • Symplectic correctors
    • J. E. Marsden, G. W. Patrick, and W. F. Shadwick, eds., American Mathematical Society, Providence, RI
    • J. WISDOM, M. HOLMAN, AND J. TOUMA, Symplectic correctors, in Integration Algorithms and Classical Mechanics, J. E. Marsden, G. W. Patrick, and W. F. Shadwick, eds., American Mathematical Society, Providence, RI, 1996.
    • (1996) Integration Algorithms and Classical Mechanics
    • Wisdom, J.1    Holman, M.2    Touma, J.3
  • 10
    • 0000328310 scopus 로고
    • A numerical algorithm for Hamiltonian systems
    • G. ROWLANDS, A numerical algorithm for Hamiltonian systems, J. Comput. Phys., 97 (1991), pp. 235-239.
    • (1991) J. Comput. Phys. , vol.97 , pp. 235-239
    • Rowlands, G.1
  • 11
    • 0042239760 scopus 로고
    • Improved Trotter-like formula
    • M. SUZUKI, Improved Trotter-like formula, Phys. Lett. A, 180 (1993), pp. 232-234.
    • (1993) Phys. Lett. A , vol.180 , pp. 232-234
    • Suzuki, M.1
  • 12
    • 0042388997 scopus 로고
    • A molecular dynamics simulation of a water droplet by the implicit-Euler/Langevin scheme
    • T. SCHLICK, S. FIGUEROA, AND M. MEZEI, A molecular dynamics simulation of a water droplet by the implicit-Euler/Langevin scheme, J. Chem. Phys., 94 (1991), pp. 2118-2129.
    • (1991) J. Chem. Phys. , vol.94 , pp. 2118-2129
    • Schlick, T.1    Figueroa, S.2    Mezei, M.3
  • 13
    • 85050535270 scopus 로고
    • Optimization methods in computational chemistry
    • K. B. Lipkowitz and D. B. Boyd, eds., VCH Publishers, New York
    • T. SCHLICK, Optimization methods in computational chemistry, in Reviews in Computational Chemistry, vol. III, K. B. Lipkowitz and D. B. Boyd, eds., VCH Publishers, New York, 1992, pp. 1-71.
    • (1992) Reviews in Computational Chemistry , vol.3 , pp. 1-71
    • Schlick, T.1
  • 14
    • 0004318070 scopus 로고
    • Sur les trajectoires des corpuscles életrisés
    • C. STÖRMER, Sur les trajectoires des corpuscles életrisés, Arch. Sci., 24 (1907) pp. 5-18, 113-158, 221-247.
    • (1907) Arch. Sci. , vol.24 , pp. 5-18
    • Störmer, C.1
  • 15
    • 11744344265 scopus 로고
    • Hamiltonians for discrete dynamics
    • S. TOXVAERD, Hamiltonians for discrete dynamics, Phys. Rev. E, 50 (1994), pp. 2271-2274.
    • (1994) Phys. Rev. E , vol.50 , pp. 2271-2274
    • Toxvaerd, S.1
  • 16
    • 21344493594 scopus 로고
    • Molecular dynamics and time reversibility
    • D. LEVESQUE AND L. VERLET, Molecular dynamics and time reversibility, J. Statist. Phys., 72 (1993), pp. 519-537.
    • (1993) J. Statist. Phys. , vol.72 , pp. 519-537
    • Levesque, D.1    Verlet, L.2
  • 18
    • 22944467757 scopus 로고
    • Computer "experiments" on condensed fluids I. Thermodynamical properties of Lennard-Jones molecules
    • L. VERLET, Computer "experiments" on condensed fluids I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev., 159 (1967), pp. 98-103.
    • (1967) Phys. Rev. , vol.159 , pp. 98-103
    • Verlet, L.1
  • 19
    • 85052507481 scopus 로고
    • Clarendon Press, Oxford, reprinted with corrections in paperback in 1989
    • M. P. ALLEN AND D. J. TILDESLEY, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987; reprinted with corrections in paperback in 1989.
    • (1987) Computer Simulation of Liquids
    • Allen, M.P.1    Tildesley, D.J.2
  • 21
    • 0007148604 scopus 로고
    • Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme
    • M. MANDZIUK AND T. SCHLICK, Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme, Chem. Phys. Lett., 237 (1995), pp. 525-535.
    • (1995) Chem. Phys. Lett. , vol.237 , pp. 525-535
    • Mandziuk, M.1    Schlick, T.2
  • 22
    • 0002945485 scopus 로고
    • Error analysis for a class of methods for stiff nonlinear initial value problems
    • Dundee 1975, G. A. Watson, ed., Springer-Verlag, Berlin
    • G. DAHLQUIST, Error analysis for a class of methods for stiff nonlinear initial value problems, in Numerical Analysis, Dundee 1975, G. A. Watson, ed., Springer-Verlag, Berlin, 1975, pp. 60-74.
    • (1975) Numerical Analysis , pp. 60-74
    • Dahlquist, G.1
  • 24
    • 0001564321 scopus 로고
    • Dangers of multiple-time-step methods
    • J. J. BIESIADECKI and R. D. SKEEL, Dangers of multiple-time-step methods, J. Comput. Phys., 109 (1993), pp. 318-328.
    • (1993) J. Comput. Phys. , vol.109 , pp. 318-328
    • Biesiadecki, J.J.1    Skeel, R.D.2
  • 25
    • 84963146276 scopus 로고
    • Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions
    • H. GRUBMÜLLER, H. HELLER, A. WINDEMUTH, AND K. SCHULTEN, Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molecular Sim., 6 (1991), pp. 121-142.
    • (1991) Molecular Sim. , vol.6 , pp. 121-142
    • Grubmüller, H.1    Heller, H.2    Windemuth, A.3    Schulten, K.4
  • 26
    • 33646650705 scopus 로고
    • Reversible multiple time scale molecular dynamics
    • M. TUCKERMAN, B. J. BERNE, AND G. J. MARTYNA, Reversible multiple time scale molecular dynamics, J. Chem. Phys., 97 (1992), pp. 1990-2001.
    • (1992) J. Chem. Phys. , vol.97 , pp. 1990-2001
    • Tuckerman, M.1    Berne, B.J.2    Martyna, G.J.3
  • 27
    • 0142080331 scopus 로고
    • Increasing the time step in molecular dynamics
    • A. NYBERG AND T. SCHLICK, Increasing the time step in molecular dynamics, Chem. Phys. Lett., 198 (1992), pp. 538-546.
    • (1992) Chem. Phys. Lett. , vol.198 , pp. 538-546
    • Nyberg, A.1    Schlick, T.2
  • 28
    • 49549156305 scopus 로고
    • The modified equation approach to the stability and accuracy analysis of finite difference methods
    • R. F. WARMING AND B. J. HYETT, The modified equation approach to the stability and accuracy analysis of finite difference methods, J. Comput. Phys., 14 (1974), pp. 159-179.
    • (1974) J. Comput. Phys. , vol.14 , pp. 159-179
    • Warming, R.F.1    Hyett, B.J.2
  • 29
    • 85033311189 scopus 로고    scopus 로고
    • On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry
    • to appear
    • O. GONZALEZ AND J. C. SIMO, On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry, Comput. Methods Appl. Mech. Engrg., to appear.
    • Comput. Methods Appl. Mech. Engrg.
    • Gonzalez, O.1    Simo, J.C.2
  • 30
    • 0028447554 scopus 로고
    • Model problems in numerical stability theory for initial value problems
    • A. M. STUART AND A. R. HUMPHRIES, Model problems in numerical stability theory for initial value problems, SIAM Rev., 36 (1994), pp. 226-257.
    • (1994) SIAM Rev. , vol.36 , pp. 226-257
    • Stuart, A.M.1    Humphries, A.R.2
  • 31
    • 0026939543 scopus 로고
    • Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics
    • J. C. SIMO, N. TARNOW, AND K. K. WONG, Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics, Comput. Methods Appl. Mech. Engrg., 100 (1991), pp. 63-116.
    • (1991) Comput. Methods Appl. Mech. Engrg. , vol.100 , pp. 63-116
    • Simo, J.C.1    Tarnow, N.2    Wong, K.K.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.