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Volumn 84, Issue 6, 2007, Pages 847-869

On the multisymplecticity of partitioned Runge-Kutta and splitting methods

Author keywords

Multi Hamiltonian; Multisymplectic; Nonlinear Schrdinger equation; Runge Kutta methods; Splitting methods

Indexed keywords

HAMILTONIANS; NONLINEAR EQUATIONS; NUMERICAL METHODS; RUNGE KUTTA METHODS;

EID: 34547553661     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160701458633     Document Type: Article
Times cited : (39)

References (28)
  • 2
    • 33646234930 scopus 로고    scopus 로고
    • Geometric Integrators for ODEs
    • McLachlan, R. and Quispel, G., 2006, Geometric Integrators for ODEs. Journal of Physics A, 39(19), 5251-5285.
    • (2006) Journal of Physics A , vol.39 , Issue.19 , pp. 5251-5285
    • McLachlan, R.1    Quispel, G.2
  • 3
    • 0037832748 scopus 로고    scopus 로고
    • Multi-Symplectic Integrators: Numerical schemes for Hamiltonian PDEs that conserve symplecticity
    • Bridges, T. and Reich, S., 2001, Multi-Symplectic Integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Physics Letters A, 284, 184-193.
    • (2001) Physics Letters A , vol.284 , pp. 184-193
    • Bridges, T.1    Reich, S.2
  • 4
    • 34547508162 scopus 로고    scopus 로고
    • Multisymplectic Integration
    • PhD thesis, Massey University, Palmerston North, New Zealand in preparation
    • Ryland, B.N., Multisymplectic Integration. PhD thesis, Massey University, Palmerston North, New Zealand (in preparation).
    • Ryland, B.N.1
  • 6
    • 33645984826 scopus 로고    scopus 로고
    • 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., 2006, Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients. Applied Numerical Mathematics, 56(6), 814-843.
    • (2006) Applied Numerical Mathematics , vol.56 , Issue.6 , pp. 814-843
    • Hong, J.1    Liu, Y.2    Munthe-Kaas, H.3    Zanna, A.4
  • 7
    • 33645743266 scopus 로고    scopus 로고
    • Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations
    • Liu, H. and Zhang, K., 2006, Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations. IMA Journal of Numerical Analysis, 26(2), 252-271.
    • (2006) IMA Journal of Numerical Analysis , vol.26 , Issue.2 , pp. 252-271
    • Liu, H.1    Zhang, K.2
  • 8
    • 27144436424 scopus 로고    scopus 로고
    • A multisymplectic integrator for the periodic nonlinear Schrödinger equation
    • Chen, J.B., 2005, A multisymplectic integrator for the periodic nonlinear Schrödinger equation. Applied Mathematics and Computation, 170(2), 1394-1417.
    • (2005) Applied Mathematics and Computation , vol.170 , Issue.2 , pp. 1394-1417
    • Chen, J.B.1
  • 9
    • 4344660059 scopus 로고    scopus 로고
    • Numerical study of the soliton waves of the coupled nonlinear Schrödinger system
    • Sun, J.Q., Gu, X.Y. and Ma, Z.Q., 2004, Numerical study of the soliton waves of the coupled nonlinear Schrödinger system. Physica D, 196(3-4), 311-328.
    • (2004) Physica D , vol.196 , Issue.3-4 , pp. 311-328
    • Sun, J.Q.1    Gu, X.Y.2    Ma, Z.Q.3
  • 10
    • 0142216144 scopus 로고    scopus 로고
    • Multi-symplectic methods for the coupled ID nonlinear Schrödinger system
    • Sun, J.Q. and Qin, M.Z., 2003, Multi-symplectic methods for the coupled ID nonlinear Schrödinger system. Computer Physics Communications, 155(3), 221-235.
    • (2003) Computer Physics Communications , vol.155 , Issue.3 , pp. 221-235
    • Sun, J.Q.1    Qin, M.Z.2
  • 11
    • 0036644593 scopus 로고    scopus 로고
    • A multisymplectic variational integrator for the nonlinear Schrödinger equation
    • Chen, J. and Qin, M., 2002, A multisymplectic variational integrator for the nonlinear Schrödinger equation. Numerical Methods for Partial Differential Equations, 18, 523-536.
    • (2002) Numerical Methods for Partial Differential Equations , vol.18 , pp. 523-536
    • Chen, J.1    Qin, M.2
  • 12
    • 0036532037 scopus 로고    scopus 로고
    • Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation
    • Chen, J., Qin, M. and Tang, Y., 2002, Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation. Computers and Mathematics with Applications, 43(8-9), 1095-1106.
    • (2002) Computers and Mathematics with Applications , vol.43 , Issue.8-9 , pp. 1095-1106
    • Chen, J.1    Qin, M.2    Tang, Y.3
  • 13
    • 0035841060 scopus 로고    scopus 로고
    • Geometric integrators for the nonlinear Schrödinger equation
    • Islas, A., Karpeev, D. and Schober, C., 2001, Geometric integrators for the nonlinear Schrödinger equation. Journal of Computational Physics, 173(1), 116-148.
    • (2001) Journal of Computational Physics , vol.173 , Issue.1 , pp. 116-148
    • Islas, A.1    Karpeev, D.2    Schober, C.3
  • 14
    • 0035892442 scopus 로고    scopus 로고
    • New schemes for the nonlinear Shrödinger equation
    • Chen, J., 2001, New schemes for the nonlinear Shrödinger equation. Applied Mathematics and Computations, 124(3), 371-379.
    • (2001) Applied Mathematics and Computations , vol.124 , Issue.3 , pp. 371-379
    • Chen, J.1
  • 15
    • 34447250005 scopus 로고    scopus 로고
    • Solving the nonlinear Schrödinger equation using exponential integrators
    • Berland, H., Owren, B. and Skaflestad, B., 2006, Solving the nonlinear Schrödinger equation using exponential integrators. Modeling, Identifications and Control, 27, 201-217.
    • (2006) Modeling, Identifications and Control , vol.27 , pp. 201-217
    • Berland, H.1    Owren, B.2    Skaflestad, B.3
  • 16
    • 0001668244 scopus 로고
    • Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations
    • Hardin, R.H. and Tappert, F.D., 1973, Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations. SIAM Review, 15, 423.
    • (1973) SIAM Review , vol.15 , pp. 423
    • Hardin, R.H.1    Tappert, F.D.2
  • 17
    • 1042304391 scopus 로고    scopus 로고
    • Multisymplectic box schemes and the Korteweg-de Vries Equation
    • Ascher, U. and McLachlan, R., 2004, Multisymplectic box schemes and the Korteweg-de Vries Equation. Applied Numerical Mathematics, 48, 255-269.
    • (2004) Applied Numerical Mathematics , vol.48 , pp. 255-269
    • Ascher, U.1    McLachlan, R.2
  • 18
    • 85009774577 scopus 로고    scopus 로고
    • The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs
    • Hong, J., Liu, Y. and Sun, G., 2005, The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs. Mathematics of Computation, 75, 167-181.
    • (2005) Mathematics of Computation , vol.75 , pp. 167-181
    • Hong, J.1    Liu, Y.2    Sun, G.3
  • 19
    • 0000545837 scopus 로고    scopus 로고
    • Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
    • Jay, L.O., 1996, Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems. SIAM Journal of Numerical Analysis, 33(1), 368-387.
    • (1996) SIAM Journal of Numerical Analysis , vol.33 , Issue.1 , pp. 368-387
    • Jay, L.O.1
  • 21
    • 0000300459 scopus 로고
    • Numerically induced chaos in the nonlinear Schrödinger equation
    • Ablowitz, M.J. and Herbst, B.M., 1989, Numerically induced chaos in the nonlinear Schrödinger equation. Physics Review Letters, 62(18), 2065-2068.
    • (1989) Physics Review Letters , vol.62 , Issue.18 , pp. 2065-2068
    • Ablowitz, M.J.1    Herbst, B.M.2
  • 22
    • 0037400187 scopus 로고    scopus 로고
    • Multi-symplectic methods for generalized Schrödinger equations
    • Islas, A. and Schober, C., 2003, Multi-symplectic methods for generalized Schrödinger equations. Future Generation Computer Systems, 19, 403-413.
    • (2003) Future Generation Computer Systems , vol.19 , pp. 403-413
    • Islas, A.1    Schober, C.2
  • 25
    • 1042263828 scopus 로고    scopus 로고
    • Geometric space-time integration of ferromagnetic materials
    • Frank, J., 2004, Geometric space-time integration of ferromagnetic materials. Applied Numerical Mathematics, 48, 307-322.
    • (2004) Applied Numerical Mathematics , vol.48 , pp. 307-322
    • Frank, J.1
  • 26
    • 0031270094 scopus 로고    scopus 로고
    • Optimal stability polynomials for splitting methods, with application to the time-dependent Schröder equation
    • Gray, S. and McLachlan, R.I., 1997, Optimal stability polynomials for splitting methods, with application to the time-dependent Schröder equation. Applied Numerical Mathematics, 25, 275-286.
    • (1997) Applied Numerical Mathematics , vol.25 , pp. 275-286
    • Gray, S.1    McLachlan, R.I.2
  • 27
    • 33646271105 scopus 로고    scopus 로고
    • Numerical methods for Hamiltonian PDEs
    • Bridges, T. and Reich, S., 2006, Numerical methods for Hamiltonian PDEs. Journal of Physics A, 39, 5287-5320.
    • (2006) Journal of Physics A , vol.39 , pp. 5287-5320
    • Bridges, T.1    Reich, S.2
  • 28
    • 0039152065 scopus 로고    scopus 로고
    • Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
    • Bridges, T. and Reich, S., 2001, Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations. Physica D, 152, 491-504.
    • (2001) Physica D , vol.152 , pp. 491-504
    • Bridges, T.1    Reich, S.2


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