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Volumn 48, Issue 3-4, 2004, Pages 255-269

Multisymplectic box schemes and the Korteweg-de Vries equation

Author keywords

Box scheme; Hamiltonian system; Korteweg de Vries equation; Multisymplectic method; Symplectic method

Indexed keywords

BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; HAMILTONIANS; INTEGRATION; MATHEMATICAL MODELS; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); THEOREM PROVING;

EID: 1042304391     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2003.09.002     Document Type: Conference Paper
Times cited : (144)

References (19)
  • 2
    • 0001737039 scopus 로고
    • Implicit-explicit methods for time-dependent PDE's
    • Ascher U., Ruuth S., Wetton B. Implicit-explicit methods for time-dependent PDE's. SIAM J. Numer. Anal. 32:1995;797-823.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 797-823
    • Ascher, U.1    Ruuth, S.2    Wetton, B.3
  • 3
    • 0031269714 scopus 로고    scopus 로고
    • Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
    • Ascher U., Ruuth S., Spiteri R. Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25:1997;151-167.
    • (1997) Appl. Numer. Math. , vol.25 , pp. 151-167
    • Ascher, U.1    Ruuth, S.2    Spiteri, R.3
  • 4
    • 1042300924 scopus 로고    scopus 로고
    • Geometric integration and its applications
    • P.G. Ciarlet, & F. Cucker. Amsterdam: North-Holland
    • Budd C.J., Piggott M.D. Geometric integration and its applications. Ciarlet P.G., Cucker F. Handbook of Numerical Analysis XI. 2003;35-139 North-Holland, Amsterdam.
    • (2003) Handbook of Numerical Analysis XI , pp. 35-139
    • Budd, C.J.1    Piggott, M.D.2
  • 5
    • 0037832748 scopus 로고    scopus 로고
    • Multi-symplectic integrators: Numerical schemes for Hamiltonian PDEs that conserve symplecticity
    • Bridges T.J., Reich S. Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Phys. Lett. A. 284:(4-5):2001;184-193.
    • (2001) Phys. Lett. A , vol.284 , Issue.4-5 , pp. 184-193
    • Bridges, T.J.1    Reich, S.2
  • 6
    • 0036556457 scopus 로고    scopus 로고
    • Square-conservative schemes for a class of evolution equations using Lie-group methods
    • Chen J.B., Munthe-Kaas H., Qin M.Z. Square-conservative schemes for a class of evolution equations using Lie-group methods. SIAM J. Numer. Anal. 39:(6):2002;2164-2178.
    • (2002) SIAM J. Numer. Anal. , vol.39 , Issue.6 , pp. 2164-2178
    • Chen, J.B.1    Munthe-Kaas, H.2    Qin, M.Z.3
  • 7
    • 1042277672 scopus 로고
    • On an oscillation phenomenon in the numerical solution of the diffusion-convection equation
    • Fisk R.S. On an oscillation phenomenon in the numerical solution of the diffusion-convection equation. SIAM J. Numer. Anal. 19:(4):1982;721-724.
    • (1982) SIAM J. Numer. Anal. , vol.19 , Issue.4 , pp. 721-724
    • Fisk, R.S.1
  • 9
    • 84990609933 scopus 로고
    • Dispersive approximation in fluid dynamics
    • Hou T.Y., Lax P.D. Dispersive approximation in fluid dynamics. Comm. Pure Appl. Math. 44:1991;1-40.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 1-40
    • Hou, T.Y.1    Lax, P.D.2
  • 11
    • 0000958123 scopus 로고
    • A new difference scheme for parabolic problems
    • J. Bramble. SYNSPADE 1970, Proc. Sympos., Univ. of Maryland, College Park, Md., 1970. New York: Academic Press
    • Keller H.B. A new difference scheme for parabolic problems. Bramble J. Numerical Solution of Partial Differential Equations, vol. II. SYNSPADE 1970, Proc. Sympos., Univ. of Maryland, College Park, Md., 1970 :1971;327-350 Academic Press, New York.
    • (1971) Numerical Solution of Partial Differential Equations , vol.2 , pp. 327-350
    • Keller, H.B.1
  • 12
    • 84990575581 scopus 로고
    • The small dispersion limit of the Korteweg-de Vries Equation: I,II,III
    • Lax P.D., Levermore C.D. The small dispersion limit of the Korteweg-de Vries Equation: I,II,III. Comm. Pure Appl. Math. 36:1983;253-290. 571-593, 809-829.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 253-290
    • Lax, P.D.1    Levermore, C.D.2
  • 13
    • 0032476963 scopus 로고    scopus 로고
    • Multisymplectic geometry, variational integrators, and nonlinear PDEs
    • Marsden J.E., Patrick G.W., Shkoller S. Multisymplectic geometry, variational integrators, and nonlinear PDEs. Comm. Math. Phys. 199:(2):1998;351-395.
    • (1998) Comm. Math. Phys. , vol.199 , Issue.2 , pp. 351-395
    • Marsden, J.E.1    Patrick, G.W.2    Shkoller, S.3
  • 14
    • 34249766017 scopus 로고
    • Symplectic integration of Hamiltonian wave equations
    • McLachlan R.I. Symplectic integration of Hamiltonian wave equations. Numer. Math. 66:(4):1994;465-492.
    • (1994) Numer. Math. , vol.66 , Issue.4 , pp. 465-492
    • Mclachlan, R.I.1
  • 16
  • 17
    • 0034687898 scopus 로고    scopus 로고
    • Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
    • Reich S. Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations. J. Comput. Phys. 157:(2):2000;473-499.
    • (2000) J. Comput. Phys. , vol.157 , Issue.2 , pp. 473-499
    • Reich, S.1
  • 18
    • 0039165805 scopus 로고    scopus 로고
    • The small dispersion limit for a nonlinear semidiscrete system of equation
    • Turner C.V., Rosales R.R. The small dispersion limit for a nonlinear semidiscrete system of equation. Stud. Appl. Math. 99:1997;205-254.
    • (1997) Stud. Appl. Math. , vol.99 , pp. 205-254
    • Turner, C.V.1    Rosales, R.R.2
  • 19
    • 0034640067 scopus 로고    scopus 로고
    • Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation
    • Zhao P.F., Qin M.Z. Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation. J. Phys. A. 33:(18):2000;3613-3626.
    • (2000) J. Phys. A , vol.33 , Issue.18 , pp. 3613-3626
    • Zhao, P.F.1    Qin, M.Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.