-
1
-
-
84873474064
-
New families of symplectic splitting methods for numerical integration in dynamical astronomy
-
doi: 10. 1016/j. apnum. 2013. 01. 003
-
Blanes, S., Casas, F., Farrés, A., Laskar, J., Makazaga, J., Murua, A.: New families of symplectic splitting methods for numerical integration in dynamical astronomy. Appl. Number. Math. (2013). doi: 10. 1016/j. apnum. 2013. 01. 003.
-
(2013)
Appl. Number. Math.
-
-
Blanes, S.1
Casas, F.2
Farrés, A.3
Laskar, J.4
Makazaga, J.5
Murua, A.6
-
2
-
-
0003171736
-
A symplectic integration algorithm for separable hamiltonian functions
-
Candy, J., Rozmus, W.: A symplectic integration algorithm for separable hamiltonian functions. J. Comput. Phys. 92(1), 230-256 (1991).
-
(1991)
J. Comput. Phys.
, vol.92
, Issue.1
, pp. 230-256
-
-
Candy, J.1
Rozmus, W.2
-
3
-
-
0000103879
-
A hybrid symplectic integrator that permits close encounters between massive bodies
-
Chambers, J. E.: A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Notices R. Astron. Soc. 304, 793-799 (1999).
-
(1999)
Mon. Notices R. Astron. Soc.
, vol.304
, pp. 793-799
-
-
Chambers, J.E.1
-
4
-
-
22844455619
-
Pseudo-high-order symplectic integrators
-
Chambers, J. E., Murison, M. A.: Pseudo-high-order symplectic integrators. Astron. J. 119(1), 425 (2000).
-
(2000)
Astron. J.
, vol.119
, Issue.1
, pp. 425
-
-
Chambers, J.E.1
Murison, M.A.2
-
5
-
-
0004240380
-
-
2nd Edition, revised and enlarged. XII Willmann-Bell, London
-
Danby, J. M. A.: Fundamentals of Celestial Mechanics. 2nd Edition, revised and enlarged. XII, p. 484. Willmann-Bell, London (1992).
-
(1992)
Fundamentals of Celestial Mechanics
, pp. 484
-
-
Danby, J.M.A.1
-
6
-
-
0001687417
-
A multiple time step symplectic algorithm for integrating close encounters
-
Duncan, M. J., Levison, H. F., Lee, M. H.: A multiple time step symplectic algorithm for integrating close encounters. Astrono. J. 116, 2067-2077 (1998).
-
(1998)
Astrono. J.
, vol.116
, pp. 2067-2077
-
-
Duncan, M.J.1
Levison, H.F.2
Lee, M.H.3
-
7
-
-
80355133246
-
The INPOP10a planetary ephemeris and its applications in fundamental physics
-
Fienga, A., Laskar, J., Kuchynka, P., Manche, H., Desvignes, G., Gastineau, M., Cognard, I., Theureau, G.: The INPOP10a planetary ephemeris and its applications in fundamental physics. Celest. Mech. Dyn. Astron. 111, 363-385 (2011).
-
(2011)
Celest. Mech. Dyn. Astron.
, vol.111
, pp. 363-385
-
-
Fienga, A.1
Laskar, J.2
Kuchynka, P.3
Manche, H.4
Desvignes, G.5
Gastineau, M.6
Cognard, I.7
Theureau, G.8
-
8
-
-
0000310133
-
On the fates of minor bodies in the outer solar system
-
Gladman, B., Duncan, M.: On the fates of minor bodies in the outer solar system. Astron. J. 100, 1680-1693 (1990).
-
(1990)
Astron. J.
, vol.100
, pp. 1680-1693
-
-
Gladman, B.1
Duncan, M.2
-
9
-
-
0041184489
-
Nth-order operator splitting schemes and nonreversible systems
-
Goldman, D., Kaper, T.: Nth-order operator splitting schemes and nonreversible systems. SIAM J. Numer. Anal. 33, 349-367 (1996).
-
(1996)
SIAM J. Numer. Anal.
, vol.33
, pp. 349-367
-
-
Goldman, D.1
Kaper, T.2
-
10
-
-
0003835647
-
-
2nd edn., Berlin: Springer
-
Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations, 2nd edn. Springer, Berlin (2006).
-
(2006)
Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations
-
-
Hairer, E.1
Lubich, C.2
Wanner, G.3
-
11
-
-
84943347456
-
Pracniques: further remarks on reducing truncation errors
-
Kahan, W.: Pracniques: further remarks on reducing truncation errors. Commun. ACM 8, 40 (1965).
-
(1965)
Commun. ACM
, vol.8
, pp. 40
-
-
Kahan, W.1
-
12
-
-
34249921769
-
Symplectic integrators and their application to dynamical astronomy
-
Kinoshita, H., Yoshida, H., Nakai, H.: Symplectic integrators and their application to dynamical astronomy. Celest. Mech. Dyn. Astron. 50, 59-71 (1991).
-
(1991)
Celest. Mech. Dyn. Astron.
, vol.50
, pp. 59-71
-
-
Kinoshita, H.1
Yoshida, H.2
Nakai, H.3
-
14
-
-
84957797799
-
Relations among lie formal series and construction of symplectic integrators
-
In: Cohen, G. D., Mora, T., Moreno, O. (eds.) 10th International symposium, (AAECC-10), San Juan de Puerto Rico, Puerto Rico, May 10-14, 1993, proceedings. Lect. Not. Comp. Sci Springer, New York
-
Koseleff, P. V.: Relations among lie formal series and construction of symplectic integrators. In: Cohen, G. D., Mora, T., Moreno, O. (eds.) Applied Algebra, Algebraic Algorithms and Error Correcting Codes. 10th International symposium, (AAECC-10), San Juan de Puerto Rico, Puerto Rico, May 10-14, 1993, proceedings. Lect. Not. Comp. Sci, vol 673, pp. 213-230. Springer, New York (1993b).
-
(1993)
Applied Algebra, Algebraic Algorithms and Error Correcting Codes
, vol.673
, pp. 213-230
-
-
Koseleff, P.V.1
-
15
-
-
0013365502
-
Exhaustive search of symplectic integrators using computer algebra. Integration algorithms and classical mechanics, Fields Inst
-
Koseleff, P. V.: Exhaustive search of symplectic integrators using computer algebra. Integration algorithms and classical mechanics, Fields Inst. Commun. 10, 103-120 (1996).
-
(1996)
Commun.
, vol.10
, pp. 103-120
-
-
Koseleff, P.V.1
-
16
-
-
0001192298
-
A numerical experiment on the chaotic behaviour of the solar system
-
Laskar, J.: A numerical experiment on the chaotic behaviour of the solar system. Nature 338, 237 (1989).
-
(1989)
Nature
, vol.338
, pp. 237
-
-
Laskar, J.1
-
17
-
-
33750108107
-
The chaotic motion of the solar system-a numerical estimate of the size of the chaotic zones
-
Laskar, J.: The chaotic motion of the solar system-a numerical estimate of the size of the chaotic zones. Icarus 88, 266-291 (1990a).
-
(1990)
Icarus
, vol.88
, pp. 266-291
-
-
Laskar, J.1
-
18
-
-
0041309326
-
-
(Goutelas, France, 1989), Editions Frontières, chap Systèmes de Variables et Eléments
-
Laskar, J.: Les Méthodes Modernes de la Mecánique Céleste (Goutelas, France, 1989), Editions Frontières, chap Systèmes de Variables et Eléments, pp. 63-87 (1990b).
-
(1990)
Les Méthodes Modernes de la Mecánique Céleste
, pp. 63-87
-
-
Laskar, J.1
-
19
-
-
0347248516
-
Analytical framework in poincaré variables for the motion of the solar system
-
In: Roy, A. (ed.) NATO, Plenum Press, ASI
-
Laskar, J.: Analytical framework in poincaré variables for the motion of the solar system. In: Roy, A. (ed.) Predictability, Stability, and Chaos in N-Body Dynamical Systems, pp. 93-114. NATO, Plenum Press, ASI (1991).
-
(1991)
Predictability, Stability, and Chaos in N-Body Dynamical Systems
, pp. 93-114
-
-
Laskar, J.1
-
20
-
-
0013366568
-
High order symplectic integrators for perturbed hamiltonian systems
-
Laskar, J., Robutel, P.: High order symplectic integrators for perturbed hamiltonian systems. Celest. Mech. Dyn. Astron. 80, 39-62 (2001).
-
(2001)
Celest. Mech. Dyn. Astron.
, vol.80
, pp. 39-62
-
-
Laskar, J.1
Robutel, P.2
-
21
-
-
0041025814
-
Confirmation of resonant structure in the solar system
-
Laskar, J., Quinn, T., Tremaine, S.: Confirmation of resonant structure in the solar system. Icarus 95, 148-152 (1992).
-
(1992)
Icarus
, vol.95
, pp. 148-152
-
-
Laskar, J.1
Quinn, T.2
Tremaine, S.3
-
22
-
-
3342916070
-
A long-term numerical solution for the insolation quantities of the earth
-
Laskar, J., Robutel, P., Joutel, F., Gastineau, M., Correia, A. C. M., Levrard, B.: A long-term numerical solution for the insolation quantities of the earth. Astron. Astrophys. 428, 261-285 (2004).
-
(2004)
Astron. Astrophys.
, vol.428
, pp. 261-285
-
-
Laskar, J.1
Robutel, P.2
Joutel, F.3
Gastineau, M.4
Correia, A.C.M.5
Levrard, B.6
-
23
-
-
79960784998
-
La2010: a new orbital solution for the long-term motion of the earth
-
Laskar, J., Fienga, A., Gastineau, M., Manche, H.: La2010: a new orbital solution for the long-term motion of the earth. Astron. Astrophys. 532, 89 (2011a).
-
(2011)
Astron. Astrophys.
, vol.532
, pp. 89
-
-
Laskar, J.1
Fienga, A.2
Gastineau, M.3
Manche, H.4
-
24
-
-
79960348227
-
Strong chaos induced by close encounters with ceres and vesta
-
Laskar, J., Gastineau, M., Delisle, J. B., Farrés, A., Fienga, A.: Strong chaos induced by close encounters with ceres and vesta. Astron. Astrophys. 532, L4 (2011b).
-
(2011)
Astron. Astrophys.
, vol.532
-
-
Laskar, J.1
Gastineau, M.2
Delisle, J.B.3
Farrés, A.4
Fienga, A.5
-
25
-
-
84923598898
-
The neogene period
-
In: Gradstein, F., Ogg, J., Smith, A. (eds.) Cambridge University Press, UK
-
Lourens, L. J., Hilgen, F. J., Shackleton, N. J., Laskar, J., Wilson, D.: The neogene period. In: Gradstein, F., Ogg, J., Smith, A. (eds.) A Geologic. Time scale, pp 409-440. Cambridge University Press, UK (2004).
-
(2004)
A Geologic. Time scale
, pp. 409-440
-
-
Lourens, L.J.1
Hilgen, F.J.2
Shackleton, N.J.3
Laskar, J.4
Wilson, D.5
-
26
-
-
0000593506
-
Composition methods in the presence of small parameters
-
McLachlan, R. I.: Composition methods in the presence of small parameters. BIT Numer. Math. 35, 258-268 (1995).
-
(1995)
BIT Numer. Math.
, vol.35
, pp. 258-268
-
-
McLachlan, R.I.1
-
27
-
-
0036439360
-
Families of high-order composition methods
-
McLachlan, R. I.: Families of high-order composition methods. Numer. Algorithms 31, 233-246 (2002).
-
(2002)
Numer. Algorithms
, vol.31
, pp. 233-246
-
-
McLachlan, R.I.1
-
29
-
-
0003532481
-
Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem
-
Serbe, Belgrade
-
Milankovitch, M.: Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem. Spec. Acad. R, Serbe, Belgrade (1941).
-
(1941)
Spec. Acad. R
-
-
Milankovitch, M.1
-
30
-
-
0036434676
-
Modern integrations of solar system dynamics
-
Morbidelli, A.: Modern integrations of solar system dynamics. Annu. Rev. Earth Planet. Sci. 30, 89-112 (2002).
-
(2002)
Annu. Rev. Earth Planet. Sci.
, vol.30
, pp. 89-112
-
-
Morbidelli, A.1
-
31
-
-
0346338471
-
Order conditions for numerical integrators obtained by composing simpler integrators
-
Murua, A., Sanz-Serna, J.: Order conditions for numerical integrators obtained by composing simpler integrators. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 357(1754), 1079-1100 (1999).
-
(1999)
Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.
, vol.357
, Issue.1754
, pp. 1079-1100
-
-
Murua, A.1
Sanz-Serna, J.2
-
32
-
-
0000871980
-
A three million year integration of the earth's orbit
-
Quinn, T. R., Tremaine, S., Duncan, M.: A three million year integration of the earth's orbit. Astron. J. 101, 2287-2305 (1991).
-
(1991)
Astron. J.
, vol.101
, pp. 2287-2305
-
-
Quinn, T.R.1
Tremaine, S.2
Duncan, M.3
-
33
-
-
0039929135
-
Long-term planetary integration with individual time steps
-
Saha, P., Tremaine, S.: Long-term planetary integration with individual time steps. Astron. J. 108, 1962-1969 (1994).
-
(1994)
Astron. J.
, vol.108
, pp. 1962-1969
-
-
Saha, P.1
Tremaine, S.2
-
34
-
-
0013403652
-
Solving linear partial differential equations by exponential splitting
-
Sheng, Q.: Solving linear partial differential equations by exponential splitting. IMA J. Numer. Anal. 9, 199-212 (1989).
-
(1989)
IMA J. Numer. Anal.
, vol.9
, pp. 199-212
-
-
Sheng, Q.1
-
35
-
-
0002845649
-
Chaotic evolution of the solar system
-
Sussman, G. J., Wisdom, J.: Chaotic evolution of the solar system. Science 257, 56-62 (1992).
-
(1992)
Science
, vol.257
, pp. 56-62
-
-
Sussman, G.J.1
Wisdom, J.2
-
36
-
-
4244036883
-
Fractal decomposition of exponential operators with applications to many-body theories and monte carlo simulations
-
Suzuki, M.: Fractal decomposition of exponential operators with applications to many-body theories and monte carlo simulations. Phys. Lett. A 146(6), 319-323 (1990).
-
(1990)
Phys. Lett. A
, vol.146
, Issue.6
, pp. 319-323
-
-
Suzuki, M.1
-
37
-
-
0001753297
-
General theory of fractal path integrals with applications to many-body theories and statistical physics
-
Suzuki, M.: General theory of fractal path integrals with applications to many-body theories and statistical physics. J. Math. Phys. 32(2), 400-407 (1991).
-
(1991)
J. Math. Phys.
, vol.32
, Issue.2
, pp. 400-407
-
-
Suzuki, M.1
-
38
-
-
4243635078
-
Lie-poisson integrators for rigid body dynamics in the solar system
-
Touma, J., Wisdom, J.: Lie-poisson integrators for rigid body dynamics in the solar system. Astron. J. 107, 1189-1202 (1994).
-
(1994)
Astron. J.
, vol.107
, pp. 1189-1202
-
-
Touma, J.1
Wisdom, J.2
-
39
-
-
0041417594
-
How many timesteps for a cycle? Analysis of the Wisdom-Holman algorithm
-
Viswanath, D.: How many timesteps for a cycle? Analysis of the Wisdom-Holman algorithm. BIT Numer. Math. 42, 194-205 (2002).
-
(2002)
BIT Numer. Math.
, vol.42
, pp. 194-205
-
-
Viswanath, D.1
-
40
-
-
33744454930
-
Symplectic correctors for canonical heliocentric n-body maps
-
Wisdom, J.: Symplectic correctors for canonical heliocentric n-body maps. Astron. J. 131(4), 2294 (2006).
-
(2006)
Astron. J.
, vol.131
, Issue.4
, pp. 2294
-
-
Wisdom, J.1
-
41
-
-
0346444651
-
Symplectic maps for the n-body problem
-
Wisdom, J., Holman, M.: Symplectic maps for the n-body problem. Astron. J. 102, 1528-1538 (1991).
-
(1991)
Astron. J.
, vol.102
, pp. 1528-1538
-
-
Wisdom, J.1
Holman, M.2
-
42
-
-
0002613398
-
Symplectic correctors
-
Wisdom, J., Holman, M., Touma, J.: Symplectic correctors. Fields Inst. Commun. 10, 217 (1996).
-
(1996)
Fields Inst. Commun.
, vol.10
, pp. 217
-
-
Wisdom, J.1
Holman, M.2
Touma, J.3
-
43
-
-
0001005075
-
Construction of higher order symplectic integrators
-
Yoshida, H.: Construction of higher order symplectic integrators. Phys. Lett. A 150(5-7), 262-268 (1990).
-
(1990)
Phys. Lett. A
, vol.150
, Issue.5-7
, pp. 262-268
-
-
Yoshida, H.1
|