메뉴 건너뛰기




Volumn , Issue , 2006, Pages 71-113

A survey of multi-symplectic runge-kutta type methods for hamiltonian partial differential equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34249890092     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812774194_0005     Document Type: Chapter
Times cited : (13)

References (41)
  • 1
    • 24644472743 scopus 로고
    • Linear Crank-Nicholsen scheme for nonlinear Dirac equations
    • A. Alvarez, Linear Crank-Nicholsen scheme for nonlinear Dirac equations, J. Comput. Phys. 99 (1992) 348-350.
    • (1992) J. Comput. Phys. , vol.99 , pp. 348-350
    • Alvarez, A.1
  • 2
    • 0008447599 scopus 로고
    • Interaction dynamics for the solitary waves of a nonlinear Dirac model
    • A. Alvarez and B. Carreras, Interaction dynamics for the solitary waves of a nonlinear Dirac model, Phys. Lett. 86A (1981) 327-332.
    • (1981) Phys. Lett , vol.86A , pp. 327-332
    • Alvarez, A.1    Carreras, B.2
  • 3
    • 0348059253 scopus 로고
    • The numerical study of a nonliear one-dimensional Dirac equation
    • A. Alvarez, P. Kuo and L. Vazquez, The numerical study of a nonliear one-dimensional Dirac equation, Appl. Math. Comput. 13 (1983) 1-15.
    • (1983) Appl. Math. Comput. , vol.13 , pp. 1-15
    • Alvarez, A.1    Kuo, P.2    Vazquez, L.3
  • 4
    • 1042304391 scopus 로고    scopus 로고
    • Multisymplectic box schemes and the Korteweg-de Vries equation
    • U. Ascher and R. McLachlan, Multisymplectic box schemes and the Korteweg-de Vries equation, Appl. Numer. Math. 48 (2004) 2550-269.
    • (2004) Appl. Numer. Math. , vol.48 , pp. 2550-2269
    • Ascher, U.1    McLachlan, R.2
  • 6
    • 0042137401 scopus 로고    scopus 로고
    • Muti-symplectic structures and wave propagation
    • T. J. Bridges, Muti-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
  • 7
    • 0037832748 scopus 로고    scopus 로고
    • Multi-symplectic integrator: Numerical schemes for Hamiltonian PDEs that conserve symplecticity
    • T. J. Bridges and S. Reich, Multi-symplectic integrator: numerical schemes for Hamiltonian PDEs that conserve symplecticity, Physics Letters A 284 (2001) 184-193.
    • (2001) Physics Letters A , vol.284 , pp. 184-193
    • Bridges, T.J.1    Reich, S.2
  • 8
    • 0035892442 scopus 로고    scopus 로고
    • New schemes for the nonlinear Schrodinger equation
    • J. Chen, New schemes for the nonlinear Schrodinger equation, Appl. Math. Comput. 124 (2001) 371-379.
    • (2001) Appl. Math. Comput. , vol.124 , pp. 371-379
    • Chen, J.1
  • 9
    • 0002211850 scopus 로고
    • Stability of Runge-Kutta methods for trajectory problems
    • G. J. Cooper, Stability of Runge-Kutta methods for trajectory problems, IMA J. Numer. Anal. 7 (1987) 1-13.
    • (1987) IMA J. Numer. Anal. , vol.7 , pp. 1-13
    • Cooper, G.J.1
  • 10
    • 0001686631 scopus 로고    scopus 로고
    • Symplectic finite difference approximations of the nonlinear Klein-Gordon equation
    • D. B. Duncan, Symplectic finite difference approximations of the nonlinear Klein-Gordon equation, SIAM J. Numer. Anal. 34 (1997) 1742-1760.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1742-1760
    • Duncan, D.B.1
  • 13
    • 0039657874 scopus 로고
    • Split-step spectral schemes for nonlinear Dirac systems
    • J. de Frutos & J. M. Sanz-Serna, Split-step spectral schemes for nonlinear Dirac systems, J. Comp. Phys. 83 (1989) 407-423.
    • (1989) J. Comp. Phys. , vol.83 , pp. 407-423
    • de Frutos, J.1    Sanz-Serna, J.M.2
  • 15
    • 3543095217 scopus 로고    scopus 로고
    • Multisymplecticity of the central box scheme for a class of Hamiltonian PDEs and an application to quasi-periodic solitary waves
    • J. Hong and Y. Liu, Multisymplecticity of the central box scheme for a class of Hamiltonian PDEs and an application to quasi-periodic solitary waves, Math. Comput. Modelling. 39 (2004) 1035-1047.
    • (2004) Math. Comput. Modelling. , vol.39 , pp. 1035-1047
    • Hong, J.1    Liu, Y.2
  • 17
    • 84867955067 scopus 로고    scopus 로고
    • A novel numerical approach to simulating nonlinear Schrodinger equation with varying coefficients
    • J. Hong and Y. Liu, A novel numerical approach to simulating nonlinear Schrodinger equation with varying coefficients, Appl. Math. Lett. 16(5) (2003), 759-765.
    • (2003) Appl. Math. Lett. , vol.16 , Issue.5 , pp. 759-765
    • Hong, J.1    Liu, Y.2
  • 21
    • 31244436460 scopus 로고    scopus 로고
    • Multi-symplecticity of the centred box discretization for Hamiltonian PDEs with m > 2 space dimensions
    • J. Hong and M. Qin, Multi-symplecticity of the centred box discretization 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
  • 23
    • 0035841060 scopus 로고    scopus 로고
    • Geometric integrators for the nonlinear Schrodinger equation
    • A.L. Islas, D. A. Karpeev and C.M. Schober, Geometric integrators for the nonlinear Schrodinger equation, J. Comput. Phys. 173 (2001) 116-148.
    • (2001) J. Comput. Phys. , vol.173 , pp. 116-148
    • Islas, A.L.1    Karpeev, D.A.2    Schober, C.M.3
  • 24
    • 3242702916 scopus 로고    scopus 로고
    • On the preservation of phase space structure under multisymplectic discretization
    • A. L. Islas and C. M. Schober, On the preservation of phase space structure under multisymplectic discretization, J. Comput. Phys. 197 (2004) 585-609.
    • (2004) J. Comput. Phys. , vol.197 , pp. 585-609
    • Islas, A.L.1    Schober, C.M.2
  • 25
    • 0011615763 scopus 로고
    • Canonical Runge-Kutta methods
    • F. M. Lasagni, Canonical Runge-Kutta methods, ZAMP 39 (1988) 952-953.
    • (1988) ZAMP , vol.39 , pp. 952-953
    • Lasagni, F.M.1
  • 26
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • J. E. Marsden & M. West, Discrete mechanics and variational integrators, Acta Numerica 10 (2001) 1-158.
    • (2001) Acta Numerica , vol.10 , pp. 1-158
    • Marsden, J.E.1    West, M.2
  • 28
    • 34249766017 scopus 로고
    • Symplectic integration of Hamiltonian wave equations
    • R. I. McLachlan, Symplectic integration of Hamiltonian wave equations, Numer. Math. 66 (1994) 465-492.
    • (1994) Numer. Math. , vol.66 , pp. 465-492
    • McLachlan, R.I.1
  • 29
    • 0037400145 scopus 로고    scopus 로고
    • Multi-symplectic integration methods for Hamiltonian PDEs
    • B. Moore and S. Reich, Multi-symplectic integration methods for Hamiltonian PDEs, Future Gener. Comput. Syst. 19 (2003) 395-402.
    • (2003) Future Gener. Comput. Syst. , vol.19 , pp. 395-402
    • Moore, B.1    Reich, S.2
  • 30
    • 0242339583 scopus 로고    scopus 로고
    • Backward error analysis for multi-symplectic integration methods
    • B. Moore and S. Reich, Backward error analysis for multi-symplectic integration methods, Numer. Math. 95 (2003) 625-652.
    • (2003) Numer. Math. , vol.95 , pp. 625-652
    • Moore, B.1    Reich, S.2
  • 31
    • 0034687898 scopus 로고    scopus 로고
    • Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
    • S. Reich, Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations, J. Comp. Phys. 157 (2000) 2, 473-499.
    • (2000) J. Comp. Phys. , vol.157 , Issue.2 , pp. 473-499
    • Reich, S.1
  • 32
    • 0038976122 scopus 로고
    • Runge-Kutta schemes for Hamiltonian systems
    • J. M. Sanz-Serna, Runge-Kutta schemes for Hamiltonian systems, BIT 28 (1988) 877-883.
    • (1988) BIT , vol.28 , pp. 877-883
    • Sanz-Serna, J.M.1
  • 33
    • 0040419824 scopus 로고
    • The numerical integration of Hamiltonian systems
    • ed. by J.R. Cash & I. Gladwell, Clarendon Press, Oxford
    • J. M. Sanz-Serna, The numerical integration of Hamiltonian systems, In: Computational Ordinary Differential Equations, ed. by J.R. Cash & I. Gladwell, Clarendon Press, Oxford, 1992, 437-449.
    • (1992) In: Computational Ordinary Differential Equations , pp. 437-449
    • Sanz-Serna, J.M.1
  • 35
    • 33144468570 scopus 로고    scopus 로고
    • A simple way of constructing symplectic Runge-Kutta methods
    • G. Sun, A simple way of constructing symplectic Runge-Kutta methods, J. Comput. Math. 18 (2000) 61-68.
    • (2000) J. Comput. Math. , vol.18 , pp. 61-68
    • Sun, G.1
  • 36
    • 0001433845 scopus 로고
    • Symplectic partitioned Runge-Kutta methods
    • G. Sun, Symplectic partitioned Runge-Kutta methods, J. Comput. Math. 11 (1993) 365-372.
    • (1993) J. Comput. Math. , vol.11 , pp. 365-372
    • Sun, G.1
  • 37
    • 0034311551 scopus 로고    scopus 로고
    • Construction of multi-symplectic schemes of any finite order for modified wave equation
    • Y. Sun and M. Qin, Construction of multi-symplectic schemes of any finite order for modified wave equation, J. Math. Phys. 41 (2000) 7854-7868.
    • (2000) J. Math. Phys. , vol.41 , pp. 7854-7868
    • Sun, Y.1    Qin, M.2
  • 38
    • 0042475779 scopus 로고
    • On the conservation of the symplectic structure in the numerical solution of Hamiltonian systems (in Russian)
    • In, ed. by S.S. Filippov, Keldysh Institute of Applied Mathematics, USSR Academy of Sciences, Moscow
    • Y. B. Suris, On the conservation of the symplectic structure in the numerical solution of Hamiltonian systems (in Russian), In: Numerical Solution of Ordinary Differential Equations, ed. by S.S. Filippov, Keldysh Institute of Applied Mathematics, USSR Academy of Sciences, Moscow, 1988, 148-160.
    • (1988) Numerical Solution of Ordinary Differential Equations , pp. 148-160
    • Suris, Y.B.1
  • 39
    • 0041473970 scopus 로고
    • Hamiltonian methods of Runge-Kutta type and their variational interpolation (in Russian)
    • Y. B. Suris, Hamiltonian methods of Runge-Kutta type and their variational interpolation (in Russian), Math. Model. 2 (1990) 78-87.
    • (1990) Math. Model. , vol.2 , pp. 78-87
    • Suris, Y.B.1
  • 40
    • 0348170697 scopus 로고    scopus 로고
    • Numerical implementation of the multi-symplectic Preissmann scheme and its equivalent schemes
    • Y. Wang, B. Wang and M. Qin, Numerical implementation of the multi-symplectic Preissmann scheme and its equivalent schemes, Appl. Math. Comput. 149 (2004) 299-326.
    • (2004) Appl. Math. Comput. , vol.149 , pp. 299-326
    • Wang, Y.1    Wang, B.2    Qin, M.3
  • 41
    • 0034640067 scopus 로고    scopus 로고
    • Multi-symplectic geometry and multi-symplectic Preissmann Scheme for the KdV equation
    • P. Zhao and M. Qin, Multi-symplectic geometry and multi-symplectic Preissmann Scheme for the KdV equation, J. Phy. A: Math. Gen. 33 (2000) 3613-3626.
    • (2000) J. Phy. A: Math. Gen. , vol.33 , pp. 3613-3626
    • Zhao, P.1    Qin, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.