-
2
-
-
33947285360
-
-
De Vogelaere, Methods of integration which preserve the contact transformation property of the Hamiltonian equations, Report 4, Department of Mathematics, University of Notre Dame, 1956.
-
-
-
-
3
-
-
0020798563
-
A canonical integration technique
-
Ruth R. A canonical integration technique. IEEE Trans. Nucl. Sci. 30 (1983) 2669-2671
-
(1983)
IEEE Trans. Nucl. Sci.
, vol.30
, pp. 2669-2671
-
-
Ruth, R.1
-
4
-
-
0002779128
-
On difference schemes and symplectic geometry
-
Feng K. (Ed), Science Press, Beijing
-
Feng K. On difference schemes and symplectic geometry. In: Feng K. (Ed). Proceeding of the 1984 Beijing Symposium on D.D. (1985), Science Press, Beijing 42-58
-
(1985)
Proceeding of the 1984 Beijing Symposium on D.D.
, pp. 42-58
-
-
Feng, K.1
-
7
-
-
0001299089
-
Difference schemes for Hamiltonian formalism and symplectic geometry
-
Feng K. Difference schemes for Hamiltonian formalism and symplectic geometry. J. Comput. Math. 4 (1986) 279-289
-
(1986)
J. Comput. Math.
, vol.4
, pp. 279-289
-
-
Feng, K.1
-
8
-
-
0002961720
-
Construct of canonical difference schemes for Hamiltonian formalism via generating functions
-
Feng K., Wu H., Qin M., and Wang D. Construct of canonical difference schemes for Hamiltonian formalism via generating functions. J. Comput. Math. 7 (1989) 71-96
-
(1989)
J. Comput. Math.
, vol.7
, pp. 71-96
-
-
Feng, K.1
Wu, H.2
Qin, M.3
Wang, D.4
-
9
-
-
0000301299
-
A symplectic difference scheme for the infinite-dimensional Hamiltonian system
-
Li C., and Qin M. A symplectic difference scheme for the infinite-dimensional Hamiltonian system. J. Comput. Math. 6 (1988) 164-174
-
(1988)
J. Comput. Math.
, vol.6
, pp. 164-174
-
-
Li, C.1
Qin, M.2
-
10
-
-
0040114714
-
Recent progress in the theory and application of symplectic integrators
-
Yoshida H. Recent progress in the theory and application of symplectic integrators. Celest. Mech. Dynam. Astronom. 56 (1993) 27-43
-
(1993)
Celest. Mech. Dynam. Astronom.
, vol.56
, pp. 27-43
-
-
Yoshida, H.1
-
12
-
-
0012152740
-
Symplectic geometry and computational Hamilton mechanics
-
Qin M. Symplectic geometry and computational Hamilton mechanics. Mech. Practice 6 (1990) 1-20
-
(1990)
Mech. Practice
, Issue.6
, pp. 1-20
-
-
Qin, M.1
-
13
-
-
0025249534
-
Multi-stage symplectic schemes of two kinds of Hamiltonian systems of wave equations
-
Qin M. Multi-stage symplectic schemes of two kinds of Hamiltonian systems of wave equations. Comput. Math. Appl. 19 (1990) 51-62
-
(1990)
Comput. Math. Appl.
, vol.19
, pp. 51-62
-
-
Qin, M.1
-
14
-
-
0026682206
-
Construction of higher order symplectic schemes by composition
-
Qin M., and Zhu W. Construction of higher order symplectic schemes by composition. Computing 47 (1991) 309-321
-
(1991)
Computing
, vol.47
, pp. 309-321
-
-
Qin, M.1
Zhu, W.2
-
15
-
-
0001005075
-
Construction of higher order symplectic integrators
-
Yoshida H. Construction of higher order symplectic integrators. Phys. Lett. A 150 (1990) 262-268
-
(1990)
Phys. Lett. A
, vol.150
, pp. 262-268
-
-
Yoshida, H.1
-
16
-
-
33947210657
-
History and present state of symplectic algorithm
-
Zeng W., and Kong L. History and present state of symplectic algorithm. J. Huaqiao Univ. 25 (2004) 113-117
-
(2004)
J. Huaqiao Univ.
, vol.25
, pp. 113-117
-
-
Zeng, W.1
Kong, L.2
-
17
-
-
33746314863
-
Symplectic integration of Hamiltonian system
-
Channell P.J., and Scovel C. Symplectic integration of Hamiltonian system. Nonlinearity 3 (1990) 231-259
-
(1990)
Nonlinearity
, vol.3
, pp. 231-259
-
-
Channell, P.J.1
Scovel, C.2
-
18
-
-
0011615763
-
Canonical Runge-Kutta methods
-
Lasagni F.M. Canonical Runge-Kutta methods. Z. Angew. Math. Phys. 39 (1988) 952-953
-
(1988)
Z. Angew. Math. Phys.
, vol.39
, pp. 952-953
-
-
Lasagni, F.M.1
-
19
-
-
0038976122
-
Runge-Kutta schemes for Hamiltonian systems
-
Sanz-Serna J.M. Runge-Kutta schemes for Hamiltonian systems. BIT 28 (1988) 877-883
-
(1988)
BIT
, vol.28
, pp. 877-883
-
-
Sanz-Serna, J.M.1
-
20
-
-
0037747984
-
On the canonicity of mappings that can be generated by methods of Runge-Kutta type for integrating systems x″ = -∂U/∂x
-
Suris Yu.B. On the canonicity of mappings that can be generated by methods of Runge-Kutta type for integrating systems x″ = -∂U/∂x. Zh. Vychisl. Mat. i Mat. Fiz. 29 (1989) 202-211
-
(1989)
Zh. Vychisl. Mat. i Mat. Fiz.
, vol.29
, pp. 202-211
-
-
Suris, Yu.B.1
-
21
-
-
0001433845
-
Symplectic partitioned Runge-Kutta methods
-
Sun G. Symplectic partitioned Runge-Kutta methods. J. Comput. Math. 11 (1993) 365-372
-
(1993)
J. Comput. Math.
, vol.11
, pp. 365-372
-
-
Sun, G.1
-
22
-
-
84968505707
-
Explicit canonical methods for Hamiltonian systems
-
Okunbor D., and Skeel R.D. Explicit canonical methods for Hamiltonian systems. Math. Comput. 59 (1992) 439-455
-
(1992)
Math. Comput.
, vol.59
, pp. 439-455
-
-
Okunbor, D.1
Skeel, R.D.2
-
23
-
-
0043164835
-
Symplectic and multi-symplectic schemes with the simple finite element method
-
Liu Z., Bai Y., Li Q., and Wu K. Symplectic and multi-symplectic schemes with the simple finite element method. Phys. Lett. A 314 (2003) 443-455
-
(2003)
Phys. Lett. A
, vol.314
, pp. 443-455
-
-
Liu, Z.1
Bai, Y.2
Li, Q.3
Wu, K.4
-
24
-
-
1042284864
-
A structure preserving discretization of nonlinear Schrödinger equation
-
Huang M., Ru Q., and Gong C. A structure preserving discretization of nonlinear Schrödinger equation. J. Comput. Math. 17 (1999) 553-560
-
(1999)
J. Comput. Math.
, vol.17
, pp. 553-560
-
-
Huang, M.1
Ru, Q.2
Gong, C.3
-
25
-
-
0032476963
-
Multi-symplectic geometry, variational integrators, and nonlinear PDEs
-
Marsden J., Patrick G.W., and Shkoller S. Multi-symplectic geometry, variational integrators, and nonlinear PDEs. Commun. Math. Phys. 199 (1998) 351-395
-
(1998)
Commun. Math. Phys.
, vol.199
, pp. 351-395
-
-
Marsden, J.1
Patrick, G.W.2
Shkoller, S.3
-
26
-
-
0042137401
-
Multi-symplectic structures and wave propagation
-
Bridges T.J. Multi-symplectic structures and wave propagation. Math. Proc. Camb. Phil. Soc. 121 (1997) 147-190
-
(1997)
Math. Proc. Camb. Phil. Soc.
, vol.121
, pp. 147-190
-
-
Bridges, T.J.1
-
27
-
-
0030695841
-
A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities
-
Bridges T.J. A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities. Proc. R. Soc. Lond. A 453 (1997) 1365-1395
-
(1997)
Proc. R. Soc. Lond. A
, vol.453
, pp. 1365-1395
-
-
Bridges, T.J.1
-
28
-
-
0037832748
-
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
-
Bridges T.J., and Recih S. Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Phys. Lett. A 284 (2001) 184-193
-
(2001)
Phys. Lett. A
, vol.284
, pp. 184-193
-
-
Bridges, T.J.1
Recih, S.2
-
29
-
-
0034687898
-
Multi-symplectic Runge-Kutta method for Hamiltonian wave equations
-
Reich S. Multi-symplectic Runge-Kutta method for Hamiltonian wave equations. J. Comput. Phys. 157 (2001) 473-499
-
(2001)
J. Comput. Phys.
, vol.157
, pp. 473-499
-
-
Reich, S.1
-
30
-
-
0043187304
-
Finite volume method for multi-symplectic PDEs
-
Reich S. Finite volume method for multi-symplectic PDEs. BIT 40 (2000) 559-582
-
(2000)
BIT
, vol.40
, pp. 559-582
-
-
Reich, S.1
-
31
-
-
0039152065
-
Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
-
Bridges T.J., and Reich S. Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations. Physica D 152-153 (2001) 491-504
-
(2001)
Physica D
, vol.152-153
, pp. 491-504
-
-
Bridges, T.J.1
Reich, S.2
-
32
-
-
84867955067
-
A novel numerical approach to simulating nonlinear Schrödinger equation with variable coefficients
-
Hong J., and Liu Y. A novel numerical approach to simulating nonlinear Schrödinger equation with variable coefficients. Appl. Math. Lett. 16 (2002) 759-765
-
(2002)
Appl. Math. Lett.
, vol.16
, pp. 759-765
-
-
Hong, J.1
Liu, Y.2
-
33
-
-
31244436460
-
Multisymplecticity of centered box discretizations for Hamiltonian PDEs with m ≥ 2 space dimensions
-
Hong J., and Qin M. Multisymplecticity of centered box discretizations for Hamiltonian PDEs with m ≥ 2 space dimensions. Appl. Math. Lett. 15 (2002) 1005-1011
-
(2002)
Appl. Math. Lett.
, vol.15
, pp. 1005-1011
-
-
Hong, J.1
Qin, M.2
-
34
-
-
0000228722
-
On coupled Klein-Gordon-Schrödinger equations
-
Tsutsumim F. On coupled Klein-Gordon-Schrödinger equations. J. Math. Anal. Appl. 66 (1978) 358-378
-
(1978)
J. Math. Anal. Appl.
, vol.66
, pp. 358-378
-
-
Tsutsumim, F.1
-
35
-
-
0005727359
-
Multi-symplectic Fourier pseudo-spectral method for the nonlinear Schrödinger equation
-
Chen J., and Qin M. Multi-symplectic Fourier pseudo-spectral method for the nonlinear Schrödinger equation. Electron. Trans. Numer. Anal. 12 (2001) 193-204
-
(2001)
Electron. Trans. Numer. Anal.
, vol.12
, pp. 193-204
-
-
Chen, J.1
Qin, M.2
-
36
-
-
20444496902
-
High-order multi-symplectic schemes for the nonlinear Klein-Gordon equation
-
Wang Y., and Wang B. High-order multi-symplectic schemes for the nonlinear Klein-Gordon equation. Appl. Math. Comput. 166 (2005) 608-632
-
(2005)
Appl. Math. Comput.
, vol.166
, pp. 608-632
-
-
Wang, Y.1
Wang, B.2
-
37
-
-
33646246487
-
multi-symplectic composition integrator of high order
-
Chen J., and Qin M. multi-symplectic composition integrator of high order. J. Comput. Math. 21 (2003) 647-656
-
(2003)
J. Comput. Math.
, vol.21
, pp. 647-656
-
-
Chen, J.1
Qin, M.2
-
38
-
-
33645984826
-
Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients
-
Hong J., Liu Y., Munthe-Kaas H., and Zanna A. Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients. Appl. Numer. Math. 56 (2006) 814-843
-
(2006)
Appl. Numer. Math.
, vol.56
, pp. 814-843
-
-
Hong, J.1
Liu, Y.2
Munthe-Kaas, H.3
Zanna, A.4
-
39
-
-
26944495302
-
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
-
Hong J., and Li C. Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations. J. Comput. Phys. 211 (2006) 448-472
-
(2006)
J. Comput. Phys.
, vol.211
, pp. 448-472
-
-
Hong, J.1
Li, C.2
-
40
-
-
0021214532
-
A symmetry regularized long wave equation
-
Seyler C.E., and Fenstermmacler D.C. A symmetry regularized long wave equation. Phys. Fluid. 27 (1984) 4-7
-
(1984)
Phys. Fluid.
, vol.27
, pp. 4-7
-
-
Seyler, C.E.1
Fenstermmacler, D.C.2
-
41
-
-
33947219283
-
Multi-symplectic quasi-spectral method and its conservation laws for SRLW equation
-
Kong L.H., Zeng W., Liu R., and Kong L.J. Multi-symplectic quasi-spectral method and its conservation laws for SRLW equation. Chin. J. Comput. Phys. 23 (2006) 29-35
-
(2006)
Chin. J. Comput. Phys.
, vol.23
, pp. 29-35
-
-
Kong, L.H.1
Zeng, W.2
Liu, R.3
Kong, L.J.4
-
42
-
-
33947269737
-
Multi-symplectic scheme of SRLW equation and its conservation laws
-
Kong L.H., Zeng W., Liu R., and Kong L.J. Multi-symplectic scheme of SRLW equation and its conservation laws. J. Univ. Sci. Tech. China 35 (2005) 770-776
-
(2005)
J. Univ. Sci. Tech. China
, vol.35
, pp. 770-776
-
-
Kong, L.H.1
Zeng, W.2
Liu, R.3
Kong, L.J.4
-
43
-
-
33749505078
-
-
L. Kong, R. Liu, Z. Xu, Numerical simulation of interaction between Schrödinger field and Klein-Gordon field by multisymplectic method, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.01.044.
-
-
-
|