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Volumn 97, Issue 3, 2004, Pages 493-535

Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations

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EID: 2942627242     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-003-0488-3     Document Type: Article
Times cited : (37)

References (31)
  • 1
    • 21344491735 scopus 로고
    • On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms
    • Benettin, G., Giorgilli, A.: On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms. J. Statist. Phys. 74, 1117-1143 (1994)
    • (1994) J. Statist. Phys. , vol.74 , pp. 1117-1143
    • Benettin, G.1    Giorgilli, A.2
  • 2
    • 0037832748 scopus 로고    scopus 로고
    • Multi-symplectic intergrators: Numerical schemes for Hamiltonian PDEs that conserve symplecticity
    • Bridges, T., Reich, S.: Multi-symplectic intergrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity. Phys. Lett. A 284, 184-193 (2001)
    • (2001) Phys. Lett. A , vol.284 , pp. 184-193
    • Bridges, T.1    Reich, S.2
  • 3
    • 0007425310 scopus 로고
    • A new approach for the analysis of vortex methods in two and three dimensions
    • Cottet, G.H.: A new approach for the analysis of vortex methods in two and three dimensions. Ann. Analysis Nonlineaire Henri Poinc. 5, 227-285 (1988)
    • (1988) Ann. Analysis Nonlineaire Henri Poinc. , vol.5 , pp. 227-285
    • Cottet, G.H.1
  • 4
    • 0031540242 scopus 로고    scopus 로고
    • Accuracy and conservation properties in numerical integration: The case of the Korteweg-de Vries equation
    • de Frutos, J., Sanz-Serna, J.M.: Accuracy and conservation properties in numerical integration: the case of the Korteweg-de Vries equation. Numer. Math. 75, 421-445 (1997)
    • (1997) Numer. Math. , vol.75 , pp. 421-445
    • De Frutos, J.1    Sanz-Serna, J.M.2
  • 5
    • 11144279715 scopus 로고    scopus 로고
    • Numerical analysis in modern scientific computing: An introduction
    • 2nd edition, Springer
    • Deuflhard, P., Hohmann, A.: Numerical Analysis in Modern Scientific Computing: An Introduction. Text in Applied Mathematics, Vol. 43, 2nd edition, Springer 2003
    • (2003) Text in Applied Mathematics , vol.43
    • Deuflhard, P.1    Hohmann, A.2
  • 6
    • 0002062139 scopus 로고    scopus 로고
    • Gevrey regularity for nonlinear analytic parabolic equations
    • Ferrari, A.B., Titi, E.S.: Gevrey regularity for nonlinear analytic parabolic equations. Commun. Partial Diff. Eqs. 23, 1-16 (1998)
    • (1998) Commun. Partial Diff. Eqs. , vol.23 , pp. 1-16
    • Ferrari, A.B.1    Titi, E.S.2
  • 8
    • 0000566698 scopus 로고
    • Backward analysis of numerical integrators and symplectic methods
    • Hairer, E.: Backward analysis of numerical integrators and symplectic methods. Ann. Numer. Math. 1, 107-132 (1994)
    • (1994) Ann. Numer. Math. , vol.1 , pp. 107-132
    • Hairer, E.1
  • 9
    • 0031505057 scopus 로고    scopus 로고
    • The life-span of backward error analysis for numerical integrators
    • Hairer, E., Lubich, C: The life-span of backward error analysis for numerical integrators. Numer. Math. 76(4), 441-462 (1997)
    • (1997) Numer. Math. , vol.76 , Issue.4 , pp. 441-462
    • Hairer, E.1    Lubich, C.2
  • 11
    • 0003304963 scopus 로고
    • Geometric theory of semilinear parabolic equations
    • Springer, New York
    • Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics 840, Springer, New York, 1983
    • (1983) Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 12
    • 0034349011 scopus 로고    scopus 로고
    • Travelling waves in a chain of coupled nonlinear oscillators
    • Iooss, G., Kirchgässner, K.: Travelling waves in a chain of coupled nonlinear oscillators. Commun. Math. Phys. 211, 439-464 (2000)
    • (2000) Commun. Math. Phys. , vol.211 , pp. 439-464
    • Iooss, G.1    Kirchgässner, K.2
  • 13
    • 0000781993 scopus 로고    scopus 로고
    • The complex Ginzburg-Landau equation as a model problem
    • AMS, Providence, Rhode Island
    • Levermore, C.D., Oliver, M.: The Complex Ginzburg-Landau Equation as a Model Problem. In: Lectures in Applied Mathematics 31, AMS, Providence, Rhode Island, 1996, pp. 141-190
    • (1996) Lectures in Applied Mathematics , vol.31 , pp. 141-190
    • Levermore, C.D.1    Oliver, M.2
  • 15
    • 0041465981 scopus 로고
    • Discrete Gevrey regularity, attractors and upper-semicontinuity for a finite difference approximation to the Ginzburg-Landau equation
    • Lord, G.J., Stuart, A.M.: Discrete Gevrey regularity, attractors and upper-semicontinuity for a finite difference approximation to the Ginzburg-Landau equation. Numer. Funct. Anal. Optimiz. 16, 1003-1047 (1995)
    • (1995) Numer. Funct. Anal. Optimiz. , vol.16 , pp. 1003-1047
    • Lord, G.J.1    Stuart, A.M.2
  • 17
    • 0032476963 scopus 로고    scopus 로고
    • Multisymplectic geometry, variational integrators, and nonlinear PDEs
    • Marsden, J.E., Patrick, G., Shkoller, S.: Multisymplectic geometry, variational integrators, and nonlinear PDEs. Commun. Math. Phys. 199, 351-395 (1998)
    • (1998) Commun. Math. Phys. , vol.199 , pp. 351-395
    • Marsden, J.E.1    Patrick, G.2    Shkoller, S.3
  • 18
    • 84959193128 scopus 로고    scopus 로고
    • Discrete mechanics and variational integrators
    • Marsden, J.E., West, M.: Discrete mechanics and variational integrators. Acta Num. 10, 357-514 (2001)
    • (2001) Acta Num. , vol.10 , pp. 357-514
    • Marsden, J.E.1    West, M.2
  • 19
    • 0037210275 scopus 로고    scopus 로고
    • Backward error analysis of a full discretisation scheme for a class of parabolic partial differential equations
    • Matthies, K.: Backward error analysis of a full discretisation scheme for a class of parabolic partial differential equations. Nonlinear Anal. Theory Methods Appl. 52, 805-826 (2003)
    • (2003) Nonlinear Anal. Theory Methods Appl. , vol.52 , pp. 805-826
    • Matthies, K.1
  • 20
    • 2942581882 scopus 로고    scopus 로고
    • Exponential averaging of Hamiltonian evolution equations
    • To appear
    • Matthies, K., Scheel, A.: Exponential averaging of Hamiltonian evolution equations. Trans. AMS. To appear
    • Trans. AMS.
    • Matthies, K.1    Scheel, A.2
  • 21
    • 2942611717 scopus 로고    scopus 로고
    • Backward error analysis for Hamiltonian PDEs with applications to nonlinear wave equations
    • To appear
    • Moore, B., Reich, S.: Backward error analysis for Hamiltonian PDEs with applications to nonlinear wave equations. Numer. Math. To appear
    • Numer. Math.
    • Moore, B.1    Reich, S.2
  • 22
    • 0021660205 scopus 로고
    • On the separation of motions in systems with rapidly rotating phase
    • Neishtadt, A.I.: On the separation of motions in systems with rapidly rotating phase. J. Appl. Math. Mech. 48, 134-139 (1984)
    • (1984) J. Appl. Math. Mech. , vol.48 , pp. 134-139
    • Neishtadt, A.I.1
  • 23
    • 0009798843 scopus 로고    scopus 로고
    • The vortex blob method as a second-grade non-Newtonian fluid
    • Oliver, M., Shkoller, S.: The vortex blob method as a second-grade non-Newtonian fluid. Commun. Partial Diff. Eqs. 26, 295-314 (2001)
    • (2001) Commun. Partial Diff. Eqs. , vol.26 , pp. 295-314
    • Oliver, M.1    Shkoller, S.2
  • 24
    • 0003316678 scopus 로고
    • Semigroups of linear operators and applications to partial differential equations
    • Springer, New York
    • Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences 44, Springer, New York, 1983
    • (1983) Applied Mathematical Sciences , vol.44
    • Pazy, A.1
  • 26
    • 2942520479 scopus 로고
    • Higher order estimates and smoothness of nonlinear wave equations
    • Reed, M.C.: Higher order estimates and smoothness of nonlinear wave equations. Proc. Am. Math. Soc. 51, 79-85 (1975)
    • (1975) Proc. Am. Math. Soc. , vol.51 , pp. 79-85
    • Reed, M.C.1
  • 27
    • 0001444647 scopus 로고    scopus 로고
    • Backward error analysis for numerical integrators
    • Reich, S.: Backward error analysis for numerical integrators. SIAM J. Numer. Anal. 36(5), 1549-1570 (1999)
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.5 , pp. 1549-1570
    • Reich, S.1
  • 28
    • 2942515543 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. Com. Phys. 156, 1-27 (1999)
    • (1999) J. Com. Phys. , vol.156 , pp. 1-27
    • Reich, S.1
  • 29
    • 84971897259 scopus 로고
    • Symplectic integrators for Hamiltonian problems: An overview
    • Sanz-Serna, J.: Symplectic integrators for Hamiltonian problems: An overview. Acta Numerica 1, 243-286 (1992)
    • (1992) Acta Numerica , vol.1 , pp. 243-286
    • Sanz-Serna, J.1
  • 30
    • 0038379503 scopus 로고
    • Does variable step size ruin a symplectic integrator?
    • Skeel, R.D., Gear, C.W.: Does variable step size ruin a symplectic integrator? Physica 060, 311-313 (1992)
    • (1992) Physica , vol.60 , pp. 311-313
    • Skeel, R.D.1    Gear, C.W.2


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