-
1
-
-
84876628057
-
-
R. Abraham, J. E. Marsden, and T. Ratiu, Manifolds, Tensor Analysis, and Applications, 2nd ed., AMS 75, Springer-Verlag, New York, 1988.
-
R. Abraham, J. E. Marsden, and T. Ratiu, Manifolds, Tensor Analysis, and Applications, 2nd ed., AMS 75, Springer-Verlag, New York, 1988.
-
-
-
-
2
-
-
84876663749
-
-
H. Berland and B. Owren. Algebraic structures on ordered rooted trees and their significance to Lie group integrators, in Group Theory and Numerical Analysis, CRM Proc. Lecture Notes, 39, pp. 49-63, Amer. Math. Soc., Providence, RI, 2005.
-
H. Berland and B. Owren. Algebraic structures on ordered rooted trees and their significance to Lie group integrators, in Group Theory and Numerical Analysis, CRM Proc. Lecture Notes, Vol. 39, pp. 49-63, Amer. Math. Soc., Providence, RI, 2005.
-
-
-
-
3
-
-
0039179700
-
Runge-Kutta methods and renormalization
-
Ch. Brouder, Runge-Kutta methods and renormalization, Eur. Phys. J. C 12 (2000), 521-534.
-
(2000)
Eur. Phys. J. C
, vol.12
, pp. 521-534
-
-
Brouder, C.1
-
4
-
-
8144231442
-
Trees, renormalization and differential equations
-
Ch. Brouder, Trees, renormalization and differential equations, BIT 44(3) (2004), 425-438.
-
(2004)
BIT
, vol.44
, Issue.3
, pp. 425-438
-
-
Brouder, C.1
-
5
-
-
0039179843
-
Coefficients for the study of Runge-Kutta integration, processes
-
J. C. Butcher, Coefficients for the study of Runge-Kutta integration, processes, J. Austr. Math. Soc. 3 (1963), 185-201.
-
(1963)
J. Austr. Math. Soc
, vol.3
, pp. 185-201
-
-
Butcher, J.C.1
-
6
-
-
84968481790
-
An algebraic theory of integration methods
-
J. C. Butcher, An algebraic theory of integration methods, Math. Comp. 26 (1972), 79-106.
-
(1972)
Math. Comp
, vol.26
, pp. 79-106
-
-
Butcher, J.C.1
-
7
-
-
0001760366
-
On the theory of analytic forms called trees
-
A. Cayley, On the theory of analytic forms called trees, Phil. Mag. 13 (1857), 19-30.
-
(1857)
Phil. Mag
, vol.13
, pp. 19-30
-
-
Cayley, A.1
-
8
-
-
0037399954
-
Commutator-free Lie group methods
-
E. Celledoni, A. Marthinsen, and B. Owren, Commutator-free Lie group methods, FGCS 19(3) (2003), 341-352.
-
(2003)
FGCS
, vol.19
, Issue.3
, pp. 341-352
-
-
Celledoni, E.1
Marthinsen, A.2
Owren, B.3
-
9
-
-
33744721734
-
An algebraic approach to invariant preserving integrators: The case of quadratic and Hamiltonian invariants
-
P. Chattier, E. Faou, and A. Murua, An algebraic approach to invariant preserving integrators: The case of quadratic and Hamiltonian invariants, Numer. Math. 103(4) (2006), 575-590.
-
(2006)
Numer. Math
, vol.103
, Issue.4
, pp. 575-590
-
-
Chattier, P.1
Faou, E.2
Murua, A.3
-
10
-
-
0032257297
-
Hopf algebras, renormalization and noncommutative geometry
-
A. Connes and D. Kreimer, Hopf algebras, renormalization and noncommutative geometry, Comm. Math. Phys. 199(1) (1998), 203-242.
-
(1998)
Comm. Math. Phys
, vol.199
, Issue.1
, pp. 203-242
-
-
Connes, A.1
Kreimer, D.2
-
11
-
-
0034349865
-
Renormalization in quantum, field theory and the Riemann-Hilbert problem, I. The Hopf algebra structure of graphs and the main theorem
-
A. Connes and D. Kreimer, Renormalization in quantum, field theory and the Riemann-Hilbert problem, I. The Hopf algebra structure of graphs and the main theorem, Comm. Math. Phys. 210(1) (2000), 249-273.
-
(2000)
Comm. Math. Phys
, vol.210
, Issue.1
, pp. 249-273
-
-
Connes, A.1
Kreimer, D.2
-
12
-
-
0032210257
-
Hopf algebras, cyclic cohomology and the transverse index theorem
-
A. Connes and H. Moscovici, Hopf algebras, cyclic cohomology and the transverse index theorem., Comm. Math. Phys. 198(1) (1998), 199-246.
-
(1998)
Comm. Math. Phys
, vol.198
, Issue.1
, pp. 199-246
-
-
Connes, A.1
Moscovici, H.2
-
13
-
-
51249166420
-
Numerical integration of ordinary differential equations on manifolds
-
P. E. Crouch and R. Grossman, Numerical integration of ordinary differential equations on manifolds, J. Nonlinear Sci. 3 (1993), 1-33.
-
(1993)
J. Nonlinear Sci
, vol.3
, pp. 1-33
-
-
Crouch, P.E.1
Grossman, R.2
-
14
-
-
0043132603
-
-
Springer-Verlag, Berlin
-
A. Dür, Möbius Functions, Incidence Algebras and Power Series Representations, Lecture Notes in Mathematics, Vol. 1202, Springer-Verlag, Berlin, 1986.
-
(1986)
Möbius Functions, Incidence Algebras and Power Series Representations
, vol.1202
-
-
Dür, A.1
-
15
-
-
0036174722
-
Les algebres de Hopf des arbres enracinés décorés, I1
-
L. Foissy, Les algebres de Hopf des arbres enracinés décorés, I1 Bull. Sci. Math. 126(3) (2002), 193-239.
-
(2002)
Bull. Sci. Math
, vol.126
, Issue.3
, pp. 193-239
-
-
Foissy, L.1
-
16
-
-
0043104439
-
Les algebres de Hopf des arbres enracinés décorés, II
-
L. Foissy, Les algebres de Hopf des arbres enracinés décorés, II, Bull. Sd. Math. 126(4) (2002), 249-288.
-
(2002)
Bull. Sd. Math
, vol.126
, Issue.4
, pp. 249-288
-
-
Foissy, L.1
-
17
-
-
38249025073
-
Hopf-algebraic structure of families of trees
-
R. Grossman and R. G. Larson, Hopf-algebraic structure of families of trees, J. Algebra 126(1) (1989), 184-210.
-
(1989)
J. Algebra
, vol.126
, Issue.1
, pp. 184-210
-
-
Grossman, R.1
Larson, R.G.2
-
18
-
-
0015960381
-
On the Butcher group and general multi-value methods
-
E. Hairer and G. Wanner, On the Butcher group and general multi-value methods, Computing (Anh. Elektron. Rechnen) 13(1) (1974), 1-15.
-
(1974)
Computing (Anh. Elektron. Rechnen)
, vol.13
, Issue.1
, pp. 1-15
-
-
Hairer, E.1
Wanner, G.2
-
19
-
-
0041862792
-
Combinatorics of rooted trees and Hopf algebras
-
M. E. Hoffman, Combinatorics of rooted trees and Hopf algebras, Trans. Amer. Math. Soc. 355(9) (2003), 3795-3811.
-
(2003)
Trans. Amer. Math. Soc
, vol.355
, Issue.9
, pp. 3795-3811
-
-
Hoffman, M.E.1
-
20
-
-
85001667552
-
Lie-group methods
-
A. Tseries, H. Z. Munthe-Kaas, S. P. Nørsett, and A. Zanna, Lie-group methods, Acta Numer. 9 (2000), 215-365.
-
(2000)
Acta Numer
, vol.9
, pp. 215-365
-
-
Tseries, A.1
Munthe-Kaas, H.Z.2
Nørsett, S.P.3
Zanna, A.4
-
21
-
-
33646035766
-
On the Hopf algebra structure of perturbative quantum field theories
-
D. Kreimer, On the Hopf algebra structure of perturbative quantum field theories, Adv. Theor. Math. Phys. 2 (1998), 303-334.
-
(1998)
Adv. Theor. Math. Phys
, vol.2
, pp. 303-334
-
-
Kreimer, D.1
-
22
-
-
34249765469
-
Conserving algorithms for the dynamics of Hamiltonian systems of Lie groups
-
D. Lewis and J. C. Simo, Conserving algorithms for the dynamics of Hamiltonian systems of Lie groups, J. Nonlinear Sci. 4 (1994), 253-299.
-
(1994)
J. Nonlinear Sci
, vol.4
, pp. 253-299
-
-
Lewis, D.1
Simo, J.C.2
-
23
-
-
44649191303
-
Conserving algorithms for the -dimensional rigid body
-
Amer. Math. Soc, Providence, RI
-
D. Lewis and J. C. Simo, Conserving algorithms for the «-dimensional rigid body, Fields Inst. Commun., Vol. 10, Amer. Math. Soc, Providence, RI, 1995.
-
(1995)
Fields Inst. Commun
, vol.10
-
-
Lewis, D.1
Simo, J.C.2
-
25
-
-
0000533036
-
Lie-Butcher theory for Runge-Kutta methods
-
H. Z. Munthe-Kaas, Lie-Butcher theory for Runge-Kutta methods, BIT 35(4) (1995), 572-587.
-
(1995)
BIT
, vol.35
, Issue.4
, pp. 572-587
-
-
Munthe-Kaas, H.Z.1
-
26
-
-
0347669558
-
Runge-Kutta methods on Lie groups
-
H. Z. Munthe-Kaas, Runge-Kutta methods on Lie groups, BIT 38(1) (1998), 92-111.
-
(1998)
BIT
, vol.38
, Issue.1
, pp. 92-111
-
-
Munthe-Kaas, H.Z.1
-
27
-
-
0032739660
-
-
H. Z. Munthe-Kaas, High order Runge-Kutta methods on manifolds, in Proceedings of the NSF/CBMS Regional Conference on Numerical Analysis of Hamiltonian Differential Equations (Golden, CO, 1997), 29,1, pp. 115-127, 1999.
-
H. Z. Munthe-Kaas, High order Runge-Kutta methods on manifolds, in Proceedings of the NSF/CBMS Regional Conference on Numerical Analysis of Hamiltonian Differential Equations (Golden, CO, 1997), Vol. 29,1, pp. 115-127, 1999.
-
-
-
-
28
-
-
0041691084
-
On enumeration problems in Lie-Butcher theory
-
H. Z. Munthe-Kaas and S. Krogstad, On enumeration problems in Lie-Butcher theory, FGCS 19(7) (2003), 1197-1205.
-
(2003)
FGCS
, vol.19
, Issue.7
, pp. 1197-1205
-
-
Munthe-Kaas, H.Z.1
Krogstad, S.2
-
31
-
-
0033077759
-
Formal series and numerical integrators, I. Systems of ODEs and symplectic integrators
-
A. Murua, Formal series and numerical integrators, I. Systems of ODEs and symplectic integrators, Appl. Numer. Math. 29(2) (1999), 221-251.
-
(1999)
Appl. Numer. Math
, vol.29
, Issue.2
, pp. 221-251
-
-
Murua, A.1
-
32
-
-
33846860618
-
The Hopf algebra of rooted trees, free Lie algebras, and Lie series
-
A. Murua, The Hopf algebra of rooted trees, free Lie algebras, and Lie series, Found. Comput. Math. 6 (2006), 387-426.
-
(2006)
Found. Comput. Math
, vol.6
, pp. 387-426
-
-
Murua, A.1
-
33
-
-
33646237562
-
Order conditions for commutator-free Lie group methods
-
B. Owren, Order conditions for commutator-free Lie group methods, J. Phys. A: Math. Gen. 39 (2006), 5585-5599.
-
(2006)
J. Phys. A: Math. Gen
, vol.39
, pp. 5585-5599
-
-
Owren, B.1
-
34
-
-
0042878746
-
Runge-Kutta methods adapted to manifolds and based on rigid frames
-
B. Owren and A. Marthinsen, Runge-Kutta methods adapted to manifolds and based on rigid frames, BIT 39(1) (1999), 116-142.
-
(1999)
BIT
, vol.39
, Issue.1
, pp. 116-142
-
-
Owren, B.1
Marthinsen, A.2
-
35
-
-
0039334812
-
Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
-
F. Panaite, Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees, Lett. Math. Phys. 51(3) (2000), 211-219.
-
(2000)
Lett. Math. Phys
, vol.51
, Issue.3
, pp. 211-219
-
-
Panaite, F.1
-
36
-
-
0003642134
-
-
Oxford University Press, New York
-
Ch. Reutenauer, Free lie Algebras, Oxford University Press, New York, 1993.
-
(1993)
Free lie Algebras
-
-
Reutenauer, C.1
-
37
-
-
2942727229
-
The on-line encyclopedia of integer sequences
-
N. J. A. Sloane, The on-line encyclopedia of integer sequences, Notices Amer. Math. Soc. 50(8) (2003), 912-915.
-
(2003)
Notices Amer. Math. Soc
, vol.50
, Issue.8
, pp. 912-915
-
-
Sloane, N.J.A.1
|