-
1
-
-
4244101731
-
Breakdown of exponential sensitivity to initial conditions: Role of the range of interactions
-
10.1103/PhysRevLett.80.5313 0031-9007
-
Anteneodo C and Tsallis C 1998 Breakdown of exponential sensitivity to initial conditions: role of the range of interactions Phys. Rev. Lett. 102 5313-6
-
(1998)
Phys. Rev. Lett.
, vol.80
, Issue.24
, pp. 5313-5316
-
-
Anteneodo, C.1
Tsallis, C.2
-
5
-
-
0033295056
-
A time-reversible variable-stepsize integrator for constrained dynamics
-
10.1137/S1064827596314194 1064-8275
-
Barth E, Leimkuhler B and Reich S 1999 A time-reversible variable-stepsize integrator for constrained dynamics SIAM J. Sci. Comput. 21 1027-44
-
(1999)
SIAM J. Sci. Comput.
, vol.21
, Issue.3
, pp. 1027-1044
-
-
Barth, E.1
Leimkuhler, B.2
Reich, S.3
-
6
-
-
0035341642
-
High order numerical integrators for differential equations using composition and processing of low order methods
-
10.1016/S0168-9274(00)00044-1 0168-9274
-
Blanes S 2001 High order numerical integrators for differential equations using composition and processing of low order methods Appl. Numer. Math. 37 289-306
-
(2001)
Appl. Numer. Math.
, vol.37
, Issue.3
, pp. 289-306
-
-
Blanes, S.1
-
8
-
-
33646259464
-
Explicit Magnus expansions for nonlinear equations
-
Blanes S and Casas F 2006 Explicit Magnus expansions for nonlinear equations J. Phys. A: Math. Gen. 39 5405-23
-
(2006)
J. Phys. A: Math. Gen.
, vol.39
, pp. 5405-5423
-
-
Blanes, S.1
Casas, F.2
-
9
-
-
0033296257
-
Symplectic integrators with processing: A general study
-
10.1137/S1064827598332497 1064-8275
-
Blanes S, Casas F and Ros J 2000 Symplectic integrators with processing: a general study SIAM J. Sci. Comput. 21 711-27
-
(2000)
SIAM J. Sci. Comput.
, vol.21
, Issue.2
, pp. 711-727
-
-
Blanes, S.1
Casas, F.2
Ros, J.3
-
10
-
-
0037485958
-
Processing symplectic methods for near-integrable Hamiltonian systems
-
10.1023/A:1008311025472 0923-2958
-
Blanes S, Casas F and Ros J 2000 Processing symplectic methods for near-integrable Hamiltonian systems Celest. Mech. Dyn. Astron. 77 17-35
-
(2000)
Celest. Mech. Dyn. Astron.
, vol.77
, Issue.1
, pp. 17-35
-
-
Blanes, S.1
Casas, F.2
Ros, J.3
-
11
-
-
0035545873
-
High-order Runge-Kutta-Nyström geometric methods with processing
-
10.1016/S0168-9274(00)00035-0 0168-9274
-
Blanes S, Casas F and Ros J 2001 High-order Runge-Kutta-Nyström geometric methods with processing Appl. Numer. Math. 39 245-59
-
(2001)
Appl. Numer. Math.
, vol.39
, Issue.3-4
, pp. 245-259
-
-
Blanes, S.1
Casas, F.2
Ros, J.3
-
12
-
-
0001292617
-
Improved high-order integrators based on the Magnus expansion
-
10.1023/A:1022311628317 0006-3835
-
Blanes S, Casas F and Ros J 2000 Improved high-order integrators based on the Magnus expansion BIT 40 434-50
-
(2000)
BIT
, vol.40
, Issue.3
, pp. 434-450
-
-
Blanes, S.1
Casas, F.2
Ros, J.3
-
13
-
-
0001648558
-
Splitting methods for non-autonomous Hamiltonian equations
-
10.1006/jcph.2001.6733 0021-9991
-
Blanes S and Moan P C 2001 Splitting methods for non-autonomous Hamiltonian equations J. Comput. Phys. 170 205-30
-
(2001)
J. Comput. Phys.
, vol.170
, Issue.1
, pp. 205-230
-
-
Blanes, S.1
Moan, P.C.2
-
14
-
-
0037095343
-
Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods
-
10.1016/S0377-0427(01)00492-7 0377-0427
-
Blanes S and Moan P C 2002 Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nyström methods J. Comput. Appl. Math. 142 313-30
-
(2002)
J. Comput. Appl. Math.
, vol.142
, Issue.2
, pp. 313-330
-
-
Blanes, S.1
Moan, P.C.2
-
15
-
-
0033247267
-
Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
-
10.1007/s002200050642 0010-3616
-
Bobenko A I and Suris Yu B 1999 Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top Commun. Math. Phys. 204 147-88
-
(1999)
Commun. Math. Phys.
, vol.204
, Issue.1
, pp. 147-188
-
-
Bobenko, A.I.1
Suris Yu., B.2
-
16
-
-
33646271105
-
Numerical method for Hamiltonian PDEs
-
Bridges T and Reich S 2006 Numerical method for Hamiltonian PDEs J. Phys. A: Math. Gen. 39 5287-320
-
(2006)
J. Phys. A: Math. Gen.
, vol.39
, pp. 5287-5320
-
-
Bridges, T.1
Reich, S.2
-
18
-
-
0000061930
-
Geometric integration: Numerical solution of differential equations on manifolds
-
10.1098/rsta.1999.0360 1364-503X A
-
Budd C J and Iserles A 1999 Geometric integration: numerical solution of differential equations on manifolds Phil. Trans. R. Soc. A 357 945-56
-
(1999)
Phil. Trans. R. Soc.
, vol.357
, Issue.1754
, pp. 945-956
-
-
Budd, C.J.1
Iserles, A.2
-
19
-
-
1042300924
-
Geometric integration and its applications
-
Budd C J and Piggott M D 2003 Geometric integration and its applications Handbook of Numerical Analysis vol 11 (Amsterdam: North-Holland) pp 35-139
-
(2003)
Handbook of Numerical Analysis
, vol.11
, pp. 35-139
-
-
Budd, C.J.1
Piggott, M.D.2
-
23
-
-
0031488281
-
Numerical solution of isospectral flows
-
10.1090/S0025-5718-97-00902-2 0025-5718
-
Calvo M P, Iserles A and Zanna A 1997 Numerical solution of isospectral flows Math. Comput. 66 1461-86
-
(1997)
Math. Comput.
, vol.66
, Issue.220
, pp. 1461-1486
-
-
Calvo, M.P.1
Iserles, A.2
Zanna, A.3
-
24
-
-
4043073404
-
Cost-efficient Lie group integrators in the RKMK class
-
10.1023/B:BITN.0000009959.29287.d4 0006-3835
-
Casas F and Owren B 2003 Cost-efficient Lie group integrators in the RKMK class BIT 43 723-42
-
(2003)
BIT
, vol.43
, Issue.4
, pp. 723-742
-
-
Casas, F.1
Owren, B.2
-
26
-
-
0000103879
-
A hybrid symplectic integrator that permits close encounters between massive bodies
-
10.1046/j.1365-8711.1999.02379.x 0035-8711
-
Chambers J E 1999 A hybrid symplectic integrator that permits close encounters between massive bodies Mon. Not. R. Astron. Soc. 304 793-9
-
(1999)
Mon. Not. R. Astron. Soc.
, vol.304
, Issue.4
, pp. 793-799
-
-
Chambers, J.E.1
-
27
-
-
0141640851
-
Symplectic integrators with complex time steps
-
10.1086/376844 0004-6256
-
Chambers J E 2003 Symplectic integrators with complex time steps Astron. J. 126 1119-26
-
(2003)
Astron. J.
, vol.126
, Issue.2
, pp. 1119-1126
-
-
Chambers, J.E.1
-
28
-
-
33744721734
-
An algebraic approach to invariant preserving integrators: The case of quadratic and Hamiltonian invariants
-
Chartier P, Faou E and Murua A An algebraic approach to invariant preserving integrators: the case of quadratic and Hamiltonian invariants Numer. Math. (submitted)
-
Numer. Math.
-
-
Chartier, P.1
Faou, E.2
Murua, A.3
-
29
-
-
0034506522
-
Higher-order force gradient symplectic algorithms
-
10.1103/PhysRevE.62.8746 1063-651X E
-
Chin S A and Kidwell D W 2000 Higher-order force gradient symplectic algorithms Phys. Rev. E 62 8746-52 (Part B)
-
(2000)
Phys. Rev.
, vol.62
, Issue.6
, pp. 8746-8752
-
-
Chin, S.A.1
Kidwell, D.W.2
-
30
-
-
0035645521
-
Non-holonomic integrators
-
0951-7715 322
-
Cortes J and Martinez S 2001 Non-holonomic integrators Nonlinearity 14 1365-92
-
(2001)
Nonlinearity
, vol.14
, Issue.5
, pp. 1365-1392
-
-
Cortes, J.1
Martinez, S.2
-
31
-
-
0002581788
-
Higher-order hybrid Monte Carlo algorithms
-
10.1103/PhysRevLett.63.9 0031-9007
-
Creutz M and Gocksch A 1989 Higher-order hybrid Monte Carlo algorithms Phys. Rev. Lett. 63 9-12
-
(1989)
Phys. Rev. Lett.
, vol.63
, Issue.1
, pp. 9-12
-
-
Creutz, M.1
Gocksch, A.2
-
32
-
-
67649382019
-
Set-oriented numerical methods for dynamical systems
-
Dellnitz M and Junge O 2002 Set-oriented numerical methods for dynamical systems Handbook of Dynamical Systems vol 2 (Amsterdam: North-Holland) pp 221-64
-
(2002)
Handbook of Dynamical Systems
, vol.2
, pp. 221-264
-
-
Dellnitz, M.1
Junge, O.2
-
33
-
-
0041451473
-
A study of extrapolation methods based on multistep schemes without parasitic solutions
-
10.1007/BF01601932 0044-2275
-
Deuflhard P 1979 A study of extrapolation methods based on multistep schemes without parasitic solutions Z. Angew. Math. Phys. 30 177-89
-
(1979)
Z. Angew. Math. Phys.
, vol.30
, Issue.2
, pp. 177-189
-
-
Deuflhard, P.1
-
34
-
-
0005055199
-
Computation of essential molecular dynamics by subdivision techniques. I. Basic concept
-
Deuflhard P, Dellnitz M, Junge O and Schütte Ch 1998 Computation of essential molecular dynamics by subdivision techniques. I. Basic concept Computational Molecular Dynamics: Challenges, Methods, Ideas (Lecture Notes in Computational Science and Engineering vol 4) ed P Deuflhard, J Hermans, B Leimkuhler, A E Mark, S Reich and R D Skeel (Berlin: Springer) pp 98-115
-
(1998)
Computational Molecular Dynamics: Challenges, Methods, Ideas
, pp. 98-115
-
-
Deuflhard, P.1
Dellnitz, M.2
Junge, O.3
Ch, S.4
-
35
-
-
21844501952
-
Finite difference models entirely inheriting continuous symmetry of original differential equations
-
10.1142/S0129183194000830 0129-1831 C
-
Dorodnitsyn V A 1994 Finite difference models entirely inheriting continuous symmetry of original differential equations Int. J. Mod. Phys. C 5 723-34
-
(1994)
Int. J. Mod. Phys.
, vol.5
, Issue.4
, pp. 723-734
-
-
Dorodnitsyn, V.A.1
-
36
-
-
0002353028
-
Dynamical systems and geometric construction of algorithms
-
Feng K and Wang D-L 1994 Dynamical systems and geometric construction of algorithms Contemporary Mathematics vol 163 (Providence: AMS) pp 1-32
-
(1994)
Contemporary Mathematics
, vol.163
, pp. 1-32
-
-
Feng, K.1
Wang, D.-L.2
-
37
-
-
0012686870
-
Variations on a theme by Euler
-
0254-9409
-
Feng K and Wang D-L 1998 Variations on a theme by Euler J. Comput. Math. 16 97-106
-
(1998)
J. Comput. Math.
, vol.16
, pp. 97-106
-
-
Feng, K.1
Wang, D.-L.2
-
38
-
-
33646228831
-
Geometric integration for particle accelerators
-
Forest E 2006 Geometric integration for particle accelerators J. Phys. A: Math. Gen. 39 5321-77
-
(2006)
J. Phys. A: Math. Gen.
, vol.39
, pp. 5321-5377
-
-
Forest, E.1
-
39
-
-
33646245528
-
Global symplectic polynomial approximation of area-preserving maps
-
Froeschle C and Lega E 1997 Global symplectic polynomial approximation of area-preserving maps J. Diff. Eqns. Appl. 3 169-84
-
(1997)
J. Diff. Eqns. Appl.
, vol.3
, pp. 169-184
-
-
Froeschle, C.1
Lega, E.2
-
40
-
-
0032226405
-
Long-time-step methods for oscillatory differential equations
-
10.1137/S1064827596313851 1064-8275
-
Garcia-Archilla B, Sanz-Serna J-M and Skeel R D 1999 Long-time-step methods for oscillatory differential equations SIAM J. Sci. Comput. 20 930-63
-
(1999)
SIAM J. Sci. Comput.
, vol.20
, Issue.3
, pp. 930-963
-
-
Garcia-Archilla, B.1
Sanz-Serna, J.-M.2
Skeel, R.D.3
-
41
-
-
0001410035
-
Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
-
0375-9601 A
-
Ge Z and Marsden J 1998 Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators Phys. Lett. A 133 135-9
-
(1998)
Phys. Lett.
, vol.133
, pp. 135-139
-
-
Ge, Z.1
Marsden, J.2
-
42
-
-
0242440718
-
The symmetry perspective. From equilibrium to chaos in phase space and physical space
-
Golubitsky M and Stewart I 2002 The symmetry perspective. From equilibrium to chaos in phase space and physical space Progress in Mathematics vol 200 (Basel: Birkhäuser Verlag)
-
(2002)
Progress in Mathematics Vol 200
-
-
Golubitsky, M.1
Stewart, I.2
-
43
-
-
33646259221
-
Non-smooth error bounds for a family of exponential integrators applied to highly oscillatory second-order differential equations
-
Grimm V and Hochbruck M 2006 Non-smooth error bounds for a family of exponential integrators applied to highly oscillatory second-order differential equations J. Phys. A: Math. Gen. 39 5495-507
-
(2006)
J. Phys. A: Math. Gen.
, vol.39
, pp. 5495-5507
-
-
Grimm, V.1
Hochbruck, M.2
-
44
-
-
29144462459
-
Geometric integration methods that preserve Lyapunov functions
-
10.1007/s10543-005-0034-z 0006-3835
-
Grimm V and Quispel G R W 2005 Geometric integration methods that preserve Lyapunov functions BIT 45 709-23
-
(2005)
BIT
, vol.45
, Issue.4
, pp. 709-723
-
-
Grimm, V.1
Quispel, G.R.W.2
-
45
-
-
44149124852
-
Geometric integration methods that unconditionally contract volume
-
0168-9274
-
Grimm V and Quispel G R W Geometric integration methods that unconditionally contract volume Appl. Numer. Math. submitted
-
Appl. Numer. Math.
-
-
Grimm, V.1
Quispel, G.R.W.2
-
46
-
-
3142580393
-
Symmetric multistep methods over long times
-
10.1007/s00211-004-0520-2 0029-599X
-
Hairer E and Lubich C 2004 Symmetric multistep methods over long times Numer. Math. 97 699-723
-
(2004)
Numer. Math.
, vol.97
, Issue.4
, pp. 699-723
-
-
Hairer, E.1
Lubich, C.2
-
48
-
-
0346830423
-
Geometric integration illustrated by the Störmer-Verlet method
-
10.1017/S0962492902000144 0962-4929
-
Hairer E, Lubich C and Wanner G 2003 Geometric integration illustrated by the Störmer-Verlet method Acta Numer. 399-450
-
(2003)
Acta Numer.
, vol.12
, pp. 399-450
-
-
Hairer, E.1
Lubich, C.2
Wanner, G.3
-
50
-
-
27844551675
-
Explicit, time reversible, adaptive step size control
-
10.1137/040606995 1064-8275
-
Hairer E and Söderlind G 2005 Explicit, time reversible, adaptive step size control SIAM J. Sci. Comput. 26 1838-51
-
(2005)
SIAM J. Sci. Comput.
, vol.26
, Issue.6
, pp. 1838-1851
-
-
Hairer, E.1
Söderlind, G.2
-
52
-
-
0032737545
-
Symplectic variable step size integration for N-body problems
-
10.1016/S0168-9274(98)00031-2 0168-9274
-
Hardy D J, Okunbor D I and Skeel R D 1999 Symplectic variable step size integration for N-body problems Appl. Numer. Math. 29 19-30
-
(1999)
Appl. Numer. Math.
, vol.29
, Issue.1
, pp. 19-30
-
-
Hardy, D.J.1
Okunbor, D.I.2
Skeel, R.D.3
-
53
-
-
0000155361
-
The accuracy of floating point summation
-
10.1137/0914050 1064-8275
-
Higham N J 1993 The accuracy of floating point summation SIAM J. Sci. Comput. 14 783-99
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, Issue.4
, pp. 783-799
-
-
Higham, N.J.1
-
54
-
-
2942576160
-
On Magnus integrators for time-dependent Schrödinger equations
-
10.1137/S0036142902403875 0036-1429
-
Hochbruck M and Lubich C 2003 On Magnus integrators for time-dependent Schrödinger equations SIAM J. Numer. Anal. 41 945-63
-
(2003)
SIAM J. Numer. Anal.
, vol.41
, Issue.3
, pp. 945-963
-
-
Hochbruck, M.1
Lubich, C.2
-
55
-
-
36749106647
-
Construction of new integrable Hamiltonians in two degrees of freedom
-
10.1063/1.525492 0022-2488
-
Holt C R 1982 Construction of new integrable Hamiltonians in two degrees of freedom J. Math. Phys. 23 1037-46
-
(1982)
J. Math. Phys.
, vol.23
, Issue.6
, pp. 1037-1046
-
-
Holt, C.R.1
-
56
-
-
2642579181
-
A variational complex for difference equations
-
10.1007/s10208-002-0071-9 1615-3375
-
Hydon P and Mansfield E L 2004 A variational complex for difference equations Found. Comput. Math. 4 187-217
-
(2004)
Found. Comput. Math.
, vol.4
, Issue.2
, pp. 187-217
-
-
Hydon, P.1
Mansfield, E.L.2
-
58
-
-
8144219702
-
On the method of neumann series for highly oscillatory equations
-
10.1023/B:BITN.0000046810.25353.95 0006-3835
-
Iserles A 2004 On the method of neumann series for highly oscillatory equations BIT 44 473-88
-
(2004)
BIT
, vol.44
, Issue.3
, pp. 473-488
-
-
Iserles, A.1
-
59
-
-
0346968523
-
On the solution of linear differential equations in Lie groups
-
10.1098/rsta.1999.0362 1364-503X A
-
Iserles A and Nørsett S P 1999 On the solution of linear differential equations in Lie groups Phil. Trans. R. Soc. A 357 983-1019
-
(1999)
Phil. Trans. R. Soc.
, vol.357
, Issue.1754
, pp. 983-1019
-
-
Iserles, A.1
Nørsett, S.P.2
-
60
-
-
0033446079
-
Approximately preserving symmetries in the numerical integration of ordinary differential equations
-
10.1017/S0956792599003927 0956-7925
-
Iserles A, McLachlan R I and Zanna A 1999 Approximately preserving symmetries in the numerical integration of ordinary differential equations Eur. J. Appl. Math. 10 419-45
-
(1999)
Eur. J. Appl. Math.
, vol.10
, Issue.5
, pp. 419-445
-
-
Iserles, A.1
McLachlan, R.I.2
Zanna, A.3
-
62
-
-
0000545837
-
Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
-
10.1137/0733019 0036-1429
-
Jay L 1996 Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems SIAM J. Numer. Anal. 33 368-87
-
(1996)
SIAM J. Numer. Anal.
, vol.33
, Issue.1
, pp. 368-387
-
-
Jay, L.1
-
63
-
-
33646232318
-
Geometric integrators for multiple time-scale simulation
-
Jia Z and Leimkuhler B 2006 Geometric integrators for multiple time-scale simulation J. Phys. A: Math. Gen. 39 5379-403
-
(2006)
J. Phys. A: Math. Gen.
, vol.39
, pp. 5379-5403
-
-
Jia, Z.1
Leimkuhler, B.2
-
65
-
-
0002961720
-
Construction of canonical difference schemes for Hamiltonian formalism via generating functions
-
0254-9409
-
Kang F, Qin M-Z, Wang D-L and Wu H-M 1989 Construction of canonical difference schemes for Hamiltonian formalism via generating functions J. Comput. Math. 7 71-96
-
(1989)
J. Comput. Math.
, vol.7
, pp. 71-96
-
-
Kang, F.1
Qin, M.-Z.2
Wang, D.-L.3
Wu, H.-M.4
-
67
-
-
1542385930
-
A time-reversible, regularized, switching integrator for the N-body problem
-
10.1137/S1064827599355566 1064-8275
-
Kværnø A and Leimkuhler B 2000 A time-reversible, regularized, switching integrator for the N-body problem SIAM J. Sci. Comput. 22 1016-35
-
(2000)
SIAM J. Sci. Comput.
, vol.22
, Issue.3
, pp. 1016-1035
-
-
Kværnø, A.1
Leimkuhler, B.2
-
68
-
-
0002569105
-
Time-reversal symmetry in dynamical systems: A survey
-
D
-
Lamb J S W and Roberts J A G 1998 Time-reversal symmetry in dynamical systems: a survey Phys. D 112 1-39
-
(1998)
Phys.
, vol.112
, pp. 1-39
-
-
Lamb, J.S.W.1
Roberts, J.A.G.2
-
69
-
-
0013366568
-
High order symplectic integrators for perturbed Hamiltonian systems
-
10.1023/A:1012098603882 0923-2958
-
Laskar J and Robutel P 2001 High order symplectic integrators for perturbed Hamiltonian systems Celest. Mech. 80 39-62
-
(2001)
Celest. Mech.
, vol.80
, Issue.1
, pp. 39-62
-
-
Laskar, J.1
Robutel, P.2
-
70
-
-
3342916070
-
A long-term numerical solution for the insolation quantities of the earth
-
10.1051/0004-6361:20041335 0004-6361
-
Laskar J, Robutel P, Joutel F, Gastineau Correia A C M and Levrard B 2004 A long-term numerical solution for the insolation quantities of the earth Astron. Astrophys. 428 261-85
-
(2004)
Astron. Astrophys.
, vol.428
, Issue.1
, pp. 261-285
-
-
Laskar, J.1
Robutel, P.2
Joutel, F.3
Gastineau Correia, A.C.M.4
Levrard, B.5
-
71
-
-
0002105056
-
A reversible averaging integrator for multiple time-scale dynamics
-
10.1006/jcph.2001.6774 0021-9991
-
Leimkuhler B and Reich S 2001 A reversible averaging integrator for multiple time-scale dynamics J. Comput. Phys. 171 95-114
-
(2001)
J. Comput. Phys.
, vol.171
, Issue.1
, pp. 95-114
-
-
Leimkuhler, B.1
Reich, S.2
-
75
-
-
0030621836
-
Explicit symplectic integrators using Hessian-vector products
-
10.1137/S1064827595288085 1064-8275
-
Lpez-Marcos M A, Sanz-Serna J M and Skeel R D 1997 Explicit symplectic integrators using Hessian-vector products SIAM J. Sci. Comput. 18 223-38
-
(1997)
SIAM J. Sci. Comput.
, vol.18
, Issue.1
, pp. 223-238
-
-
Lpez-Marcos, M.A.1
Sanz-Serna, J.M.2
Skeel, R.D.3
-
78
-
-
84959193128
-
Discrete mechanics and variational integrators
-
10.1017/S096249290100006X 0962-4929
-
Marsden J E and West M 2001 Discrete mechanics and variational integrators Acta Numer. 10 357-514
-
(2001)
Acta Numer.
, vol.10
, Issue.0
, pp. 357-514
-
-
Marsden, J.E.1
West, M.2
-
79
-
-
0001312358
-
Explicit Lie-Poisson integration and the Euler equations
-
10.1103/PhysRevLett.71.3043 0031-9007
-
McLachlan R I 1993 Explicit Lie-Poisson integration and the Euler equations Phys. Rev. Lett. 71 3043-6
-
(1993)
Phys. Rev. Lett.
, vol.71
, Issue.19
, pp. 3043-3046
-
-
McLachlan, R.I.1
-
80
-
-
0000194427
-
On the numerical integration of ordinary differential equations by symmetric composition methods
-
10.1137/0916010 1064-8275
-
McLachlan R I 1995 On the numerical integration of ordinary differential equations by symmetric composition methods SIAM J. Sci. Comput. 16 151-68
-
(1995)
SIAM J. Sci. Comput.
, vol.16
, Issue.1
, pp. 151-168
-
-
McLachlan, R.I.1
-
81
-
-
0000593506
-
Composition methods in the presence of small parameters
-
10.1007/BF01737165 0006-3835
-
McLachlan R I 1995 Composition methods in the presence of small parameters BIT 35 258-68
-
(1995)
BIT
, vol.35
, Issue.2
, pp. 258-268
-
-
McLachlan, R.I.1
-
82
-
-
0036439360
-
Families of high-order composition methods
-
10.1023/A:1021195019574 1017-1398
-
McLachlan R I 2002 Families of high-order composition methods Numer. Alg. 31 233-46
-
(2002)
Numer. Alg.
, vol.31
, pp. 233-246
-
-
McLachlan, R.I.1
-
83
-
-
0346653215
-
The accuracy of symplectic integrators
-
0951-7715 011
-
McLachlan R I and Atela P 1992 The accuracy of symplectic integrators Nonlinearity 5 541-62
-
(1992)
Nonlinearity
, vol.5
, Issue.2
, pp. 541-562
-
-
McLachlan, R.I.1
Atela, P.2
-
84
-
-
0035486310
-
Conformal Hamiltonian systems
-
10.1016/S0393-0440(01)00020-1 0393-0440
-
McLachlan R I and Perlmutter M 2001 Conformal Hamiltonian systems J. Geom. Phys. 39 276-300
-
(2001)
J. Geom. Phys.
, vol.39
, Issue.4
, pp. 276-300
-
-
McLachlan, R.I.1
Perlmutter, M.2
-
87
-
-
4043075075
-
On the nonlinear stability of symplectic integrators
-
10.1023/B:BITN.0000025088.13092.7f 0006-3835
-
McLachlan R I, Perlmutter M and Quispel G R W 2004 On the nonlinear stability of symplectic integrators BIT 44 99-117
-
(2004)
BIT
, vol.44
, Issue.1
, pp. 99-117
-
-
McLachlan, R.I.1
Perlmutter, M.2
Quispel, G.R.W.3
-
89
-
-
85095839561
-
Splitting methods
-
10.1017/S0962492902000053 0962-4929
-
McLachlan R I and Quispel G R W 2002 Splitting methods Acta Numer. 11 341-434
-
(2002)
Acta Numer.
, vol.11
, Issue.0
, pp. 341-434
-
-
McLachlan, R.I.1
Quispel, G.R.W.2
-
91
-
-
0035511340
-
What kinds of dynamics are there? Lie pseudogroups, dynamical systems, and geometric integration
-
0951-7715 315
-
McLachlan R I and Quispel G R W 2001 What kinds of dynamics are there? Lie pseudogroups, dynamical systems, and geometric integration Nonlinearity 14 1689-706
-
(2001)
Nonlinearity
, vol.14
, Issue.6
, pp. 1689-1706
-
-
McLachlan, R.I.1
Quispel, G.R.W.2
-
92
-
-
0037881858
-
Geometric integration of conservative polynomial ODEs
-
10.1016/S0168-9274(03)00022-9 0168-9274
-
McLachlan R I and Quispel G R W 2003 Geometric integration of conservative polynomial ODEs Appl. Numer. Math. 45 411-8
-
(2003)
Appl. Numer. Math.
, vol.45
, Issue.4
, pp. 411-418
-
-
McLachlan, R.I.1
Quispel, G.R.W.2
-
93
-
-
8144230742
-
Explicit geometric integration of polynomial vector fields
-
10.1023/B:BITN.0000046814.29690.62 0006-3835
-
McLachlan R I and Quispel G R W 2004 Explicit geometric integration of polynomial vector fields BIT 44 515-38
-
(2004)
BIT
, vol.44
, Issue.3
, pp. 515-538
-
-
McLachlan, R.I.1
Quispel, G.R.W.2
-
94
-
-
0348229409
-
Geometric integration using discrete gradients
-
10.1098/rsta.1999.0363 1364-503X A
-
McLachlan R I, Quispel G R W and Robidoux N 1999 Geometric integration using discrete gradients Phil. Trans. R. Soc. A 357 1021-46
-
(1999)
Phil. Trans. R. Soc.
, vol.357
, Issue.1754
, pp. 1021-1046
-
-
McLachlan, R.I.1
Quispel, G.R.W.2
Robidoux, N.3
-
95
-
-
0001127934
-
Numerical integrators that preserve symmetries and reversing symmetries
-
10.1137/S0036142995295807 0036-1429
-
McLachlan R I, Quispel G R W and Turner G S 1998 Numerical integrators that preserve symmetries and reversing symmetries SIAM J. Numer. Anal. 35 586-99
-
(1998)
SIAM J. Numer. Anal.
, vol.35
, Issue.2
, pp. 586-599
-
-
McLachlan, R.I.1
Quispel, G.R.W.2
Turner, G.S.3
-
96
-
-
0037998870
-
The algebraic entropy of classical mechanics
-
10.1063/1.1576904 0022-2488
-
McLachlan R I and Ryland B N 2003 The algebraic entropy of classical mechanics J. Math. Phys. 44 3071-87
-
(2003)
J. Math. Phys.
, vol.44
, Issue.7
, pp. 3071-3087
-
-
McLachlan, R.I.1
Ryland, B.N.2
-
97
-
-
0000438567
-
Equivariant constrained symplectic integration
-
10.1007/BF01212956 0938-8974
-
McLachlan R I and Scovel C 1995 Equivariant constrained symplectic integration J. Nonlinear Sci. 5 233-56
-
(1995)
J. Nonlinear Sci.
, vol.5
, Issue.3
, pp. 233-256
-
-
McLachlan, R.I.1
Scovel, C.2
-
100
-
-
0347931879
-
On the KAM and nekhoroshev theorems for symplectic integrators and implications for error growth
-
0951-7715 005
-
Moan P C 2004 On the KAM and nekhoroshev theorems for symplectic integrators and implications for error growth Nonlinearity 17 67-83
-
(2004)
Nonlinearity
, vol.17
, Issue.1
, pp. 67-83
-
-
Moan, P.C.1
-
103
-
-
0037139379
-
Time-discretized variational formulation of nonsmooth frictional contact
-
10.1002/nme.361 0029-5981
-
Pandolfi A, Kane C, Marsden J E and Ortiz M 2002 Time-discretized variational formulation of nonsmooth frictional contact Int. J. Numer. Methods Eng. 53 1801-29
-
(2002)
Int. J. Numer. Methods Eng.
, vol.53
, Issue.8
, pp. 1801-1829
-
-
Pandolfi, A.1
Kane, C.2
Marsden, J.E.3
Ortiz, M.4
-
105
-
-
33646237562
-
Order conditions for commutator-free Lie group methods
-
Owren B 2006 Order conditions for commutator-free Lie group methods J. Phys. A: Math. Gen. 39 5585-99
-
(2006)
J. Phys. A: Math. Gen.
, vol.39
, pp. 5585-5599
-
-
Owren, B.1
-
106
-
-
42349103813
-
Volume-preserving integrators
-
0375-9601 A
-
Quispel G R W 1995 Volume-preserving integrators Phys. Lett. A 206 226-30
-
(1995)
Phys. Lett.
, vol.206
, pp. 226-230
-
-
Quispel, G.R.W.1
-
107
-
-
33646272035
-
-
Reich S 1993 Numerical integration of the generalized Euler equations Technical Report 93-20 Department of Computer Science, University of British Columbia
-
(1993)
Technical Report 93-20
-
-
Reich, S.1
-
108
-
-
0001444647
-
Backward error analysis for numerical integrators
-
10.1137/S0036142997329797 0036-1429
-
Reich S 1993 Backward error analysis for numerical integrators SIAM J. Numer. Anal. 36 1549-70
-
(1993)
SIAM J. Numer. Anal.
, vol.36
, Issue.5
, pp. 1549-1570
-
-
Reich, S.1
-
110
-
-
0033628310
-
Resonant and diophantine step sizes in computing invariant tori of Hamiltonian systems
-
0951-7715 314
-
Shang Z J 2000 Resonant and diophantine step sizes in computing invariant tori of Hamiltonian systems Nonlinearity 13 299-308
-
(2000)
Nonlinearity
, vol.13
, Issue.1
, pp. 299-308
-
-
Shang, Z.J.1
-
111
-
-
0013403652
-
Solving linear partial differential equations by exponential splitting
-
0272-4979
-
Sheng Q 1989 Solving linear partial differential equations by exponential splitting IMA J. Numer. Anal. 9 199-212
-
(1989)
IMA J. Numer. Anal.
, vol.9
, Issue.2
, pp. 199-212
-
-
Sheng, Q.1
-
112
-
-
0042694406
-
Nonlinear stability analysis of area-preserving integrators
-
10.1137/S0036142998349527 0036-1429
-
Skeel R D and Srinivas K 2000 Nonlinear stability analysis of area-preserving integrators SIAM J. Numer. Anal. 38 129-48
-
(2000)
SIAM J. Numer. Anal.
, vol.38
, Issue.1
, pp. 129-148
-
-
Skeel, R.D.1
Srinivas, K.2
-
113
-
-
0028483709
-
A new energy and momentum conserving algorithm for the non-linear dynamics of shells
-
10.1002/nme.1620371503 0029-5981
-
Simo J C and Tarnow N 1994 A new energy and momentum conserving algorithm for the non-linear dynamics of shells Int. J. Numer. Methods Eng. 37 2527-49
-
(1994)
Int. J. Numer. Methods Eng.
, vol.37
, Issue.15
, pp. 2527-2549
-
-
Simo, J.C.1
Tarnow, N.2
-
114
-
-
27744592945
-
Derivation of symmetric composition constants for symmetric integrators
-
10.1080/10556780500140664 1055-6788
-
Sofroniou M and Spaletta G 2005 Derivation of symmetric composition constants for symmetric integrators Optimization Methods and Software 20 597-613
-
(2005)
Optimization Methods and Software
, vol.20
, Issue.4-5
, pp. 597-613
-
-
Sofroniou, M.1
Spaletta, G.2
-
116
-
-
4244036883
-
Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations
-
10.1016/0375-9601(90)90962-N 0375-9601 A
-
Suzuki M 1990 Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations Phys. Lett. A 146 319-23
-
(1990)
Phys. Lett.
, vol.146
, Issue.6
, pp. 319-323
-
-
Suzuki, M.1
-
117
-
-
2842574881
-
Monte Carlo calculations of quantum systems. II higher order correction
-
10.1143/JPSJ.53.3765 0031-9015
-
Takahashi M and Imada M 1984 Monte Carlo calculations of quantum systems. II higher order correction J. Phys. Soc. Japan 53 3765-9
-
(1984)
J. Phys. Soc. Japan
, vol.53
, Issue.11
, pp. 3765-3769
-
-
Takahashi, M.1
Imada, M.2
-
118
-
-
0037107617
-
Computing accurate Poincaré maps
-
D
-
Tucker W 2002 Computing accurate Poincaré maps Phys. D 171 127-37
-
(2002)
Phys.
, vol.171
, pp. 127-137
-
-
Tucker, W.1
-
119
-
-
22944467757
-
Computer 'experiments' on classical fluids. I thermodynamical properties of Lennard-Jones molecules
-
10.1103/PhysRev.159.98 0031-899X
-
Verlet L 1967 Computer 'experiments' on classical fluids. I thermodynamical properties of Lennard-Jones molecules Phys. Rev. 159 98-103
-
(1967)
Phys. Rev.
, vol.159
, Issue.1
, pp. 98-103
-
-
Verlet, L.1
-
120
-
-
0000264317
-
A new semiclassical initial value method for Franck-Condon spectra
-
10.1080/00268979650027289 0026-8976
-
Walton A R and Manolopoulos D E 1996 A new semiclassical initial value method for Franck-Condon spectra Mol. Phys. 87 961-78
-
(1996)
Mol. Phys.
, vol.87
, Issue.4
, pp. 961-978
-
-
Walton, A.R.1
Manolopoulos, D.E.2
-
121
-
-
0032711364
-
From symplectic integrator to Poincaré map: Spline expansion of a map generator in Cartesian coordinates
-
10.1016/S0168-9274(98)00034-8 0168-9274
-
Warnock R L and Ellison J A 1999 From symplectic integrator to Poincaré map: spline expansion of a map generator in Cartesian coordinates Appl. Numer. Math. 29 89-98
-
(1999)
Appl. Numer. Math.
, vol.29
, Issue.1
, pp. 89-98
-
-
Warnock, R.L.1
Ellison, J.A.2
-
122
-
-
0022738251
-
Split-step methods for the solution of the nonlinear Schrödinger equation
-
10.1137/0723033 0036-1429
-
Weideman J A C and Herbst B M 1986 Split-step methods for the solution of the nonlinear Schrödinger equation SIAM J. Numer. Anal. 23 485-507
-
(1986)
SIAM J. Numer. Anal.
, vol.23
, Issue.3
, pp. 485-507
-
-
Weideman, J.A.C.1
Herbst, B.M.2
-
123
-
-
0346444651
-
Symplectic maps for the N-body problem
-
10.1086/115978 0004-6256
-
Wisdom J and Holman M 1991 Symplectic maps for the N-body problem Astron. J. 102 1528-38
-
(1991)
Astron. J.
, vol.102
, Issue.4
, pp. 1528-1538
-
-
Wisdom, J.1
Holman, M.2
-
125
-
-
0001005075
-
Construction of higher order symplectic integrators
-
10.1016/0375-9601(90)90092-3 0375-9601 A
-
Yoshida H 1990 Construction of higher order symplectic integrators Phys. Lett. A 150 262-8
-
(1990)
Phys. Lett.
, vol.150
, Issue.5-7
, pp. 262-268
-
-
Yoshida, H.1
-
126
-
-
0035938234
-
Non-existence of the modified first integral by symplectic integration methods
-
10.1016/S0375-9601(01)00186-4 0375-9601 A
-
Yoshida H 2001 Non-existence of the modified first integral by symplectic integration methods Phys. Lett. A 282 276-83
-
(2001)
Phys. Lett.
, vol.282
, Issue.4-5
, pp. 276-283
-
-
Yoshida, H.1
|