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Volumn 84, Issue 6, 2007, Pages 729-747

Forward and non-forward symplectic integrators in solving classical dynamics problems

Author keywords

Forward factorization algorithms; Keplarian orbits; Splitting methods; Symplectic integrators

Indexed keywords

ALGORITHMS; OPTIMIZATION; TWO DIMENSIONAL;

EID: 34547505331     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160701458476     Document Type: Article
Times cited : (6)

References (53)
  • 1
  • 2
    • 0009086175 scopus 로고    scopus 로고
    • Department of Physics, Univeristy of Maryland, College Park preprint
    • Neri, F., Lie Algebra and Canonical Integration. Department of Physics, Univeristy of Maryland, College Park (preprint).
    • Lie Algebra and Canonical Integration
    • Neri, F.1
  • 3
    • 0002581788 scopus 로고
    • Higher-order hydrid Monte-Carlo algorithms
    • Creutz, M. and Gocksch, A., 1989, Higher-order hydrid Monte-Carlo algorithms. Physical Review Letters, 63, 9-12.
    • (1989) Physical Review Letters , vol.63 , pp. 9-12
    • Creutz, M.1    Gocksch, A.2
  • 4
    • 33646388286 scopus 로고
    • 4th-order symplectic integration
    • Forest, E. and Ruth, R.D., 1990, 4th-order symplectic integration. Physica D, 43, 105-117.
    • (1990) Physica D , vol.43 , pp. 105-117
    • Forest, E.1    Ruth, R.D.2
  • 5
    • 0001005075 scopus 로고    scopus 로고
    • Construction of higher order symplectic integrators
    • Yoshida, H., Construction of higher order symplectic integrators, Physics Letters, A150, 262-268.
    • Physics Letters , vol.A150 , pp. 262-268
    • Yoshida, H.1
  • 6
    • 0346444651 scopus 로고
    • Symplectic maps for the N-body problem
    • Wisdom, J. and Holman, M., 1991, Symplectic maps for the N-body problem. Astronomical Journal, 102, 1528-1538.
    • (1991) Astronomical Journal , vol.102 , pp. 1528-1538
    • Wisdom, J.1    Holman, M.2
  • 7
    • 0040114714 scopus 로고
    • Recent progress in the theory and application of symplectic integrators
    • Yoshida, H., 1993, Recent progress in the theory and application of symplectic integrators. Celestial Mechanics and Dynamical Astronomy, 56, 27-43.
    • (1993) Celestial Mechanics and Dynamical Astronomy , vol.56 , pp. 27-43
    • Yoshida, H.1
  • 13
    • 0013403652 scopus 로고
    • Solving linear partial differential equations by exponential splitting
    • Sheng, Q., 1989, Solving linear partial differential equations by exponential splitting. IMA Journal of Numerical Anaysis, 9, 199-212.
    • (1989) IMA Journal of Numerical Anaysis , vol.9 , pp. 199-212
    • Sheng, Q.1
  • 14
    • 0001753297 scopus 로고
    • General theory of fractal path-integrals with applications to many-body theories and statistical physics
    • Suzuki, M., 1991, General theory of fractal path-integrals with applications to many-body theories and statistical physics. Journal of Mathematical Physics, 32, 400-407.
    • (1991) Journal of Mathematical Physics , vol.32 , pp. 400-407
    • Suzuki, M.1
  • 15
    • 0041184489 scopus 로고    scopus 로고
    • Nth-order operator splitting schemes and nonreversible systems
    • Goldman, D. and Kaper, T.J., 1996, Nth-order operator splitting schemes and nonreversible systems. SIAM Journal on Numerical Analysis, 33, 349-367.
    • (1996) SIAM Journal on Numerical Analysis , vol.33 , pp. 349-367
    • Goldman, D.1    Kaper, T.J.2
  • 16
    • 2842574881 scopus 로고
    • Monte Carlo calculation of quantum systems 2 - higer order correction
    • Takahashi, M. and Imada, M., 1984, Monte Carlo calculation of quantum systems 2 - higer order correction. Journal of the Physical Society of Japan, 53, 3765-3769.
    • (1984) Journal of the Physical Society of Japan , vol.53 , pp. 3765-3769
    • Takahashi, M.1    Imada, M.2
  • 17
    • 4243960934 scopus 로고
    • Hybrid exponential product formulas for unbounded operators with possible applications to Monte Carlo simulations
    • Suzuki, M., 1995, Hybrid exponential product formulas for unbounded operators with possible applications to Monte Carlo simulations, Physics Letters, A 201, 425-428.
    • (1995) Physics Letters, A , vol.201 , pp. 425-428
    • Suzuki, M.1
  • 18
    • 0039502533 scopus 로고    scopus 로고
    • Symplectic integrators from composite operator factorizations
    • Chin, S.A., 1997, Symplectic integrators from composite operator factorizations. Physics Letters, A226, 344-348.
    • (1997) Physics Letters , vol.A226 , pp. 344-348
    • Chin, S.A.1
  • 19
    • 23844514667 scopus 로고    scopus 로고
    • New scheme of hybrid Exponential product formulas with applications to quantum. Monte Carlo simulations
    • D. Landau, K. Mon and H. Shuttler Eds, Berlin: Springler, pp
    • Suzuki, M., 1996, New scheme of hybrid Exponential product formulas with applications to quantum. Monte Carlo simulations. In: D. Landau, K. Mon and H. Shuttler (Eds), Computer Simulation Studies in Condensed Matter Physics VIII (Berlin: Springler), pp. 1-6.
    • (1996) Computer Simulation Studies in Condensed Matter Physics VIII , pp. 1-6
    • Suzuki, M.1
  • 20
    • 0000593506 scopus 로고
    • Composition methods in the presence of a small parameters
    • McLachlan, R., 1995, Composition methods in the presence of a small parameters. BIT, 35, 258-268.
    • (1995) BIT , vol.35 , pp. 258-268
    • McLachlan, R.1
  • 21
    • 18644380792 scopus 로고    scopus 로고
    • Fourth-order algorithms for solving the multivariable Langevin equation and the Kramers equation
    • Forbert, H.A. and Chin, S.A., 2001, Fourth-order algorithms for solving the multivariable Langevin equation and the Kramers equation. Physical Review, E 63, 016703.
    • (2001) Physical Review, E , vol.63 , pp. 016703
    • Forbert, H.A.1    Chin, S.A.2
  • 22
    • 0034900642 scopus 로고    scopus 로고
    • Fourth-order diffusion Monte Carlo algorithms for solving quantum manybody problems
    • Forbert, H.A. and Chin, S.A., 2001, Fourth-order diffusion Monte Carlo algorithms for solving quantum manybody problems. Physical Review, B 63, 144518.
    • (2001) Physical Review, B , vol.63 , pp. 144518
    • Forbert, H.A.1    Chin, S.A.2
  • 23
    • 33645894500 scopus 로고    scopus 로고
    • Quantum Monte Carlo: Theory and application to molecular systems
    • Aspura-Guzik, A. and Lester, WA., 2005, Quantum Monte Carlo: Theory and application to molecular systems. Advances in Quantum Chemistry, 49, 209.
    • (2005) Advances in Quantum Chemistry , vol.49 , pp. 209
    • Aspura-Guzik, A.1    Lester, W.A.2
  • 24
    • 0035886303 scopus 로고    scopus 로고
    • A fourth-order real-space algorithm for solving local Schrödinger equations
    • Auer, J., Krotscheck, E. and Chin, S.A., 2001, A fourth-order real-space algorithm for solving local Schrödinger equations. Journal of Chemical Physics, 115, 6841-6846.
    • (2001) Journal of Chemical Physics , vol.115 , pp. 6841-6846
    • Auer, J.1    Krotscheck, E.2    Chin, S.A.3
  • 25
    • 0035505130 scopus 로고    scopus 로고
    • Applications of higher order composite factorization schemes in imaginary time path integral simulations
    • Jang, S., Jang, S. and Voth, G., 2001, Applications of higher order composite factorization schemes in imaginary time path integral simulations. Journal of Chemical Physics, 115, 7832-7842.
    • (2001) Journal of Chemical Physics , vol.115 , pp. 7832-7842
    • Jang, S.1    Jang, S.2    Voth, G.3
  • 26
    • 37649032940 scopus 로고    scopus 로고
    • Quantum statistical calculations and symplectic corrector algorithms
    • Chin, S.A., 2004, Quantum statistical calculations and symplectic corrector algorithms. Physical Review, E 69, 046118.
    • (2004) Physical Review, E , vol.69 , pp. 046118
    • Chin, S.A.1
  • 27
    • 3242678974 scopus 로고    scopus 로고
    • Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo
    • Brualla, L., Sakkos, K., Boronat, J. and Casulleras, J., 2004, Higher order and infinite Trotter-number extrapolations in path integral Monte Carlo. Journal of Chemical Physics, 121, 636-643.
    • (2004) Journal of Chemical Physics , vol.121 , pp. 636-643
    • Brualla, L.1    Sakkos, K.2    Boronat, J.3    Casulleras, J.4
  • 28
    • 18644366694 scopus 로고    scopus 로고
    • Path integral ground state with a fourth-order propagator: Application to condensed helium
    • Cuervo, J.E., Roy, P.N. and Boninsegni, M., 2005, Path integral ground state with a fourth-order propagator: Application to condensed helium. Journal of Chemical Physics, 122, 114504.
    • (2005) Journal of Chemical Physics , vol.122 , pp. 114504
    • Cuervo, J.E.1    Roy, P.N.2    Boninsegni, M.3
  • 29
    • 33344460275 scopus 로고    scopus 로고
    • Worm algorithm for continuous-space path integral Monte Carlo simulations
    • Boninsegni, M., Prokofëv, N. and Svistunov, B., 2006, Worm algorithm for continuous-space path integral Monte Carlo simulations. Physical Review Letters, 96, 070601.
    • (2006) Physical Review Letters , vol.96 , pp. 070601
    • Boninsegni, M.1    Prokofëv, N.2    Svistunov, B.3
  • 30
    • 33746362849 scopus 로고    scopus 로고
    • Superfluidity and quantum melting of p-H-2 clusters
    • Mezzacapo, F. and Boninsegni, M., 2006, Superfluidity and quantum melting of p-H-2 clusters. Physical Review Letters, 97, 045301.
    • (2006) Physical Review Letters , vol.97 , pp. 045301
    • Mezzacapo, F.1    Boninsegni, M.2
  • 31
    • 0345327693 scopus 로고    scopus 로고
    • Short-time-evolved wave functions for solving quantum many-body problems
    • Ciftja, O. and Chin, S.A., 2003, Short-time-evolved wave functions for solving quantum many-body problems. Physical Review, B 68, 134510.
    • (2003) Physical Review, B , vol.68 , pp. 134510
    • Ciftja, O.1    Chin, S.A.2
  • 32
    • 28844451153 scopus 로고    scopus 로고
    • Fourth-order algorithms for solving the imaginary-time Gross-Pitaevskii equation in a rotating anisotropic trap
    • Chin, S.A. and Krotscheck, E., 2005, Fourth-order algorithms for solving the imaginary-time Gross-Pitaevskii equation in a rotating anisotropic trap. Physical Review, E 72, 036705.
    • (2005) Physical Review, E , vol.72 , pp. 036705
    • Chin, S.A.1    Krotscheck, E.2
  • 33
    • 24644479573 scopus 로고    scopus 로고
    • Fourth-order algorithms for solving local Schrodinger equations in a strong magnetic field
    • Aichinger, M., Chin, S.A. and Krotscheck, E., 2005, Fourth-order algorithms for solving local Schrodinger equations in a strong magnetic field. Computer Physics Communications, 171, 197-207.
    • (2005) Computer Physics Communications , vol.171 , pp. 197-207
    • Aichinger, M.1    Chin, S.A.2    Krotscheck, E.3
  • 34
    • 33646446726 scopus 로고    scopus 로고
    • Effects of geometry and impurities on quantum. rings in magnetic fields
    • Aichinger, M., Chin, S.A., Krotscheck, E. and Räsänen, E., 2006, Effects of geometry and impurities on quantum. rings in magnetic fields. Physical Review, B 73, 195310.
    • (2006) Physical Review, B , vol.73 , pp. 195310
    • Aichinger, M.1    Chin, S.A.2    Krotscheck, E.3    Räsänen, E.4
  • 35
    • 0034506522 scopus 로고    scopus 로고
    • Higher-order force gradient symplectic algorithms
    • Chin, S.A. and Kidwell, D.W., 2000, Higher-order force gradient symplectic algorithms. Physical Review, E 62, 8746.
    • (2000) Physical Review, E , vol.62 , pp. 8746
    • Chin, S.A.1    Kidwell, D.W.2
  • 36
    • 26944481463 scopus 로고    scopus 로고
    • Forward symplectic integrators and the long-time phase error in periodic motions
    • Scuro, S.R. and Chin, S.A., 2005, Forward symplectic integrators and the long-time phase error in periodic motions. Physical Review, E 71, 056703.
    • (2005) Physical Review, E , vol.71 , pp. 056703
    • Scuro, S.R.1    Chin, S.A.2
  • 37
    • 23844504737 scopus 로고    scopus 로고
    • Forward symplectic integrators for solving gravitational few-body problems
    • Chin, S.A. and Chen, CR., 2005, Forward symplectic integrators for solving gravitational few-body problems. Celestial Mechanics and Dynamical Astronomy, 91, 301-322.
    • (2005) Celestial Mechanics and Dynamical Astronomy , vol.91 , pp. 301-322
    • Chin, S.A.1    Chen, C.R.2
  • 38
    • 0035335815 scopus 로고    scopus 로고
    • Fourth order gradient symplectic integrator methods for solving the timedependent Schrödinger equation
    • Chin, S.A. and Chen, CR., 2001, Fourth order gradient symplectic integrator methods for solving the timedependent Schrödinger equation. Journal of Chemical Physics, 114, 7338.
    • (2001) Journal of Chemical Physics , vol.114 , pp. 7338
    • Chin, S.A.1    Chen, C.R.2
  • 39
    • 0037158141 scopus 로고    scopus 로고
    • Gradient symplectic algorithms for solving the Schrödinger equation with time-dependent potentials
    • Chin, S.A. and Chen, CR., 2002, Gradient symplectic algorithms for solving the Schrödinger equation with time-dependent potentials. Journal of Chemical Physics, 117, 1409.
    • (2002) Journal of Chemical Physics , vol.117 , pp. 1409
    • Chin, S.A.1    Chen, C.R.2
  • 40
    • 17644431987 scopus 로고    scopus 로고
    • Fourth-order factorization, of the evolution operator for timedependent potentials
    • Baye, D., Goldstein, G. and Capel, P., 2003, Fourth-order factorization, of the evolution operator for timedependent potentials. Physics Letters, A 317, 337.
    • (2003) Physics Letters, A , vol.317 , pp. 337
    • Baye, D.1    Goldstein, G.2    Capel, P.3
  • 41
    • 41349112705 scopus 로고    scopus 로고
    • Sixth-order factorization of the evolution operator for time-dependent potentials
    • Goldstein, G. and Baye, D., 2004, Sixth-order factorization of the evolution operator for time-dependent potentials. Physical Review, E 70, 056703.
    • (2004) Physical Review, E , vol.70 , pp. 056703
    • Goldstein, G.1    Baye, D.2
  • 42
    • 32044458599 scopus 로고    scopus 로고
    • Gradient Symplectic Algorithms for Solving the Radial Schrödinger Equation
    • Chin, S.A. and Anisimov, P., 2006, Gradient Symplectic Algorithms for Solving the Radial Schrödinger Equation. Journal of Chemical Physics, 124, 054106.
    • (2006) Journal of Chemical Physics , vol.124 , pp. 054106
    • Chin, S.A.1    Anisimov, P.2
  • 43
    • 45849155971 scopus 로고    scopus 로고
    • Construction, of high-order force-gradient algorithms for integration of motion in classical and quantum systems
    • Omelyan, LP., Mryglod, I.M. and Folk, R., 2002, Construction, of high-order force-gradient algorithms for integration of motion in classical and quantum systems. Physical Review, E66, 026701.
    • (2002) Physical Review , vol.E66 , pp. 026701
    • Omelyan, L.P.1    Mryglod, I.M.2    Folk, R.3
  • 44
    • 0037399891 scopus 로고    scopus 로고
    • Symplectic analytically integrable decomposition algorithms: Classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations
    • Omelyan, LR, Mryglod, I.M. and Folk, R., 2003, Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations. Computer Physics Communications, 151, 272.
    • (2003) Computer Physics Communications , vol.151 , pp. 272
    • Omelyan, L.R.1    Mryglod, I.M.2    Folk, R.3
  • 45
    • 33748949418 scopus 로고    scopus 로고
    • Extrapolated gradientlike algorithms for molecular dynamics and celestial mechanics simulations
    • Omelyan, LP., 2006, Extrapolated gradientlike algorithms for molecular dynamics and celestial mechanics simulations. Physical Review, E 74, 036703.
    • (2006) Physical Review, E , vol.74 , pp. 036703
    • Omelyan, L.P.1
  • 46
    • 34547531653 scopus 로고    scopus 로고
    • Battin, Richard H., 1999, An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition (Resten, VA: AIAA).
    • Battin, Richard H., 1999, An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition (Resten, VA: AIAA).
  • 47
    • 33847709489 scopus 로고    scopus 로고
    • Physics of symplectic integrators: Perihelion advances and symplectic corrector algorithms
    • Chin, S.A., 2007, Physics of symplectic integrators: perihelion advances and symplectic corrector algorithms. Physical Review, E 75, 036701.
    • (2007) Physical Review, E , vol.75 , pp. 036701
    • Chin, S.A.1
  • 48
    • 4244036883 scopus 로고
    • Hybrid exponential product formulas for unbounded operators with possible applications to Monte Carlo simulations
    • Suzuki, M., 1990, Hybrid exponential product formulas for unbounded operators with possible applications to Monte Carlo simulations. Physics Letters, A 146, 319-323.
    • (1990) Physics Letters, A , vol.146 , pp. 319-323
    • Suzuki, M.1
  • 49
    • 0000194427 scopus 로고
    • On the numerical integration of ordinary differential equations by symmetric composition methods
    • McLachlan, R.I., 1995, On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM Journal on Scientific Computing, 16, 151-168.
    • (1995) SIAM Journal on Scientific Computing , vol.16 , pp. 151-168
    • McLachlan, R.I.1
  • 50
    • 0036439360 scopus 로고    scopus 로고
    • Families of high-order composition methods
    • McLachlan, R.I., 2002, Families of high-order composition methods. Numerical Algorithms, 31, 233-246.
    • (2002) Numerical Algorithms , vol.31 , pp. 233-246
    • McLachlan, R.I.1
  • 51
    • 33747492396 scopus 로고    scopus 로고
    • A fundamental theorem on the structure of symplectic integrators
    • Chin, S.A., 2006, A fundamental theorem on the structure of symplectic integrators. Physics Letters, A 354, 373-376.
    • (2006) Physics Letters, A , vol.354 , pp. 373-376
    • Chin, S.A.1
  • 52
    • 33344463355 scopus 로고    scopus 로고
    • The complete characterization of fourth-order symplectic integrators with extended-linear coefficients
    • Chin, S.A., 2006, The complete characterization of fourth-order symplectic integrators with extended-linear coefficients. Physical Review, E 73, 026705.
    • (2006) Physical Review, E , vol.73 , pp. 026705
    • Chin, S.A.1
  • 53
    • 0037095343 scopus 로고    scopus 로고
    • Practical symplectic partition Runge-Kutta methods and Runge-Kutta Nyström methods
    • Blanes, S. and Moan, P.C., 2002, Practical symplectic partition Runge-Kutta methods and Runge-Kutta Nyström methods. Journal of Computational and Applied Mathematics, 142, 313-330.
    • (2002) Journal of Computational and Applied Mathematics , vol.142 , pp. 313-330
    • Blanes, S.1    Moan, P.C.2


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