메뉴 건너뛰기




Volumn 7, Issue 1, 2009, Pages 195-212

Some applications of semi-discrete variational integrators to classical field theories

Author keywords

Classical field theories; Discrete mechanics; Hamiltonian mechanics; Lagrangian mechanics; Nonlinear wave equation

Indexed keywords


EID: 84896693068     PISSN: 15755460     EISSN: 16623592     Source Type: Journal    
DOI: 10.1007/s12346-008-0011-4     Document Type: Article
Times cited : (10)

References (19)
  • 4
    • 0000226055 scopus 로고
    • Presymplectic Lagrangian systems I: The constraint algorithm and the equivalence theorem
    • M.J. Gotay, J. Nester, Presymplectic Lagrangian systems I: The constraint algorithm and the equivalence theorem, Ann. Inst. Henri Poincaré 30 (1978), 129-142.
    • (1978) Ann. Inst. Henri Poincaré , vol.30 , pp. 129-142
    • Gotay, M.J.1    Nester, J.2
  • 5
    • 0001862548 scopus 로고
    • Presymplectic Lagrangian systems II: The second order differential equation problem
    • M.J. Gotay, J. Nester, Presymplectic Lagrangian systems II: The second order differential equation problem, Ann. Inst. Henri Poincaré A 32 (1980), 1-13.
    • (1980) Ann. Inst. Henri Poincaré A , vol.32 , pp. 1-13
    • Gotay, M.J.1    Nester, J.2
  • 6
    • 0003835647 scopus 로고    scopus 로고
    • Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations
    • Springer-Verlag, Berlin, Heidelberg
    • E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Series in Computational Mathematics 31, Springer-Verlag, Berlin, Heidelberg.
    • Springer Series in Computational Mathematics 31
    • Hairer, E.1    Lubich, C.2    Wanner, G.3
  • 7
    • 0031557857 scopus 로고    scopus 로고
    • Principes of discrete time mechanics II: Classical field theory
    • G. Jaroszkiewicz, K. Norton, Principes of discrete time mechanics II: Classical field theory, J. Phys. A 30 (1997), 3145-3163.
    • (1997) J. Phys. A , vol.30 , pp. 3145-3163
    • Jaroszkiewicz, G.1    Norton, K.2
  • 8
    • 28844494719 scopus 로고    scopus 로고
    • Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press
    • B. Leimkuhler, S. Reich, Simulating Hamiltonian Dynamics, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press 2004.
    • (2004) Simulating Hamiltonian Dynamics
    • Leimkuhler, B.1    Reich, S.2
  • 9
    • 33646736110 scopus 로고    scopus 로고
    • Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids
    • Corrigendum 19 (2006), 3003-3004
    • J.C. Marrero, D. Martín de Diego, E. Martínez, Discrete Lagrangian and Hamiltonian mechanics on Lie groupoids, Nonlinearity 19 (2006), 1313-1348 and Corrigendum 19 (2006), 3003-3004.
    • (2006) Nonlinearity , vol.19 , pp. 1313-1348
    • Marrero, J.C.1    Martín de Diego, D.2    Martínez, E.3
  • 10
    • 0032476963 scopus 로고    scopus 로고
    • Multisymplectic geometry, variational ntegrators, and nonlinear PDEs
    • J. E. Marsden, G. W. Patrick, S. Shkoller, Multisymplectic geometry, variational ntegrators, and nonlinear PDEs, Commun. Math. Phys. 199 (1996), 351-395.
    • (1996) Commun. Math. Phys , vol.199 , pp. 351-395
    • Marsden, J.E.1    Patrick, G.W.2    Shkoller, S.3
  • 11
    • 0000140852 scopus 로고    scopus 로고
    • Variational methods, multisymplectic geometry and continuum mechanics
    • J. E. Marsden, S. Pekarsky, S. Shkoller, M. West, Variational methods, multisymplectic geometry and continuum mechanics, J. Geometry and Physics 38 (2001) 253-284.
    • (2001) J. Geometry and Physics , vol.38 , pp. 253-284
    • Marsden, J.E.1    Pekarsky, S.2    Shkoller, S.3    West, M.4
  • 12
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • J. E. Marsden, M. West, Discrete mechanics and variational integrators, Acta Numerica 10 (2001), 357-514.
    • (2001) Acta Numerica , vol.10 , pp. 357-514
    • Marsden, J.E.1    West, M.2
  • 13
    • 0032476963 scopus 로고    scopus 로고
    • Multisymplectic geometry, variational integrators, and nonlinear PDEs
    • J. E. Marsden, G. W. Patrick, S. Shkoller, Multisymplectic geometry, variational integrators, and nonlinear PDEs, Commun. Math. Phys. 199 (1998), 351-395.
    • (1998) Commun. Math. Phys , vol.199 , pp. 351-395
    • Marsden, J.E.1    Patrick, G.W.2    Shkoller, S.3
  • 14
    • 23744517380 scopus 로고    scopus 로고
    • Classical field theory on Lie algebroids: Variational aspects
    • E. Martínez, Classical field theory on Lie algebroids: Variational aspects, J. Phys. A: Math. Gen. 38 (2005), 7145-7160.
    • (2005) J. Phys. A: Math. Gen , vol.38 , pp. 7145-7160
    • Martínez, E.1
  • 15
    • 0000008977 scopus 로고
    • Discrete versions of some classical integrable systems and factorization of matrix polynomials
    • J. Moser, A.P. Veselov, Discrete versions of some classical integrable systems and factorization of matrix polynomials, Comm. Math. Phys. 139, (1991), 217-243.
    • (1991) Comm. Math. Phys , vol.139 , pp. 217-243
    • Moser, J.1    Veselov, A.P.2
  • 16
    • 2942627242 scopus 로고    scopus 로고
    • Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations
    • M. Oliver, M. West, C. Wulff, Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations, Numer. Math. 97 (2004), 493-535.
    • (2004) Numer. Math , vol.97 , pp. 493-535
    • Oliver, M.1    West, M.2    Wulff, C.3
  • 18
    • 33750330681 scopus 로고    scopus 로고
    • Discrete Lagrangian field theories on Lie groupoids
    • J. Vankerschaver, F. Cantrijn, Discrete Lagrangian field theories on Lie groupoids, J. Geom. and Phys. 57 (2007), 665-689.
    • (2007) J. Geom. and Phys , vol.57 , pp. 665-689
    • Vankerschaver, J.1    Cantrijn, F.2
  • 19
    • 0002859047 scopus 로고
    • Integrable discrete-time systems and difference operators
    • A.P. Veselov, Integrable discrete-time systems and difference operators, Funct. Anal. Appl. 22 (1988), 83-93.
    • (1988) Funct. Anal. Appl , vol.22 , pp. 83-93
    • Veselov, A.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.