Generation of longitudinal vibrations in piano strings: From physics to sound synthesis, The Journal of the Acoustical Society of America, vol.117, issue.4, pp.2268-2278, 2005. ,
DOI : 10.1121/1.1868212
Conservation properties of a time FE method. Part I: time-stepping schemes forN-body problems, International Journal for Numerical Methods in Engineering, vol.11, issue.5 ,
DOI : 10.1002/1097-0207(20001020)49:5<599::AID-NME960>3.0.CO;2-9
Conservation properties of a time FE method?part II: Time-stepping schemes for non-linear elastodynamics, International Journal for Numerical Methods in Engineering, vol.6, issue.8, pp.1931-1955, 2001. ,
DOI : 10.1002/nme.103
Conservative numerical methods for nonlinear strings, The Journal of the Acoustical Society of America, vol.118, issue.5, pp.3316-3327, 2005. ,
DOI : 10.1121/1.2046787
Conserved quantities of some Hamiltonian wave equations after full discretization, Numerische Mathematik, vol.103, issue.2, pp.197-223, 2006. ,
DOI : 10.1007/s00211-006-0680-3
Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: Application to the vibrating piano string, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.45-48, p.70, 2010. ,
DOI : 10.1016/j.cma.2010.04.013
URL : https://hal.archives-ouvertes.fr/inria-00534473
Explicit energy-conserving schemes for the three-body problem, Journal of Computational Physics, vol.83, issue.2, pp.485-493, 1989. ,
DOI : 10.1016/0021-9991(89)90132-0
Mathematical analysis and numerical methods for science and technology, 2000. ,
Accuracy and conservation properties in numerical integration: the case of the korteweg-de vries equation, Numerische Mathematik, vol.75, issue.4, pp.421-445, 1997. ,
Standard nearest-neighbour discretizations of Klein???Gordon models cannot preserve both energy and linear momentum, Journal of Physics A: Mathematical and General, vol.39, issue.23, pp.7217-7226, 2006. ,
DOI : 10.1088/0305-4470/39/23/003
Finite-difference schemes for nonlinear wave equation that inherit energy conservation property, Journal of Computational and Applied Mathematics, vol.134, issue.1-2, pp.37-57, 2001. ,
DOI : 10.1016/S0377-0427(00)00527-6
URL : http://doi.org/10.1016/s0377-0427(00)00527-6
Hyperbolic systems of conservation laws, 1991. ,
URL : https://hal.archives-ouvertes.fr/hal-00113734
Exact energy and momentum conserving algorithms for general models in nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.13-14, pp.1763-1783, 2000. ,
DOI : 10.1016/S0045-7825(00)00189-4
URL : https://hal.archives-ouvertes.fr/hal-01363585
On the stability of symplectic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry, Computer Methods in Applied Mechanics and Engineering, vol.134, issue.3-4, pp.197-222, 1996. ,
DOI : 10.1016/0045-7825(96)01009-2
Conservative numerical methods for, Journal of Computational Physics, vol.56, issue.1, pp.28-41, 1984. ,
DOI : 10.1016/0021-9991(84)90081-0
Conservation properties of a time FE method. Part IV: Higher order energy and momentum conserving schemes, International Journal for Numerical Methods in Engineering, vol.18, issue.13, pp.1849-1897, 2005. ,
DOI : 10.1002/nme.1339
Backward analysis of numerical integrators and symplectic methods, Ann. Numer. Math, vol.1, issue.1-4, pp.107-132, 1994. ,
The life-span of backward error analysis for numerical integrators, Numerische Mathematik, vol.76, issue.4, pp.441-462, 1997. ,
DOI : 10.1007/s002110050271
Differential equations, dynamical systems, and an introduction to chaos, p.417, 2004. ,
Formation of singularities in one-dimensional nonlinear wave propagation, Communications on Pure and Applied Mathematics, vol.5, issue.3, pp.377-405, 1974. ,
DOI : 10.1002/cpa.3160270307
Effective computational methods for wave propagation, 2008. ,
On a class of discretizations of Hamiltonian nonlinear partial differential equations, Physica D: Nonlinear Phenomena, vol.183, issue.1-2, pp.68-86, 2003. ,
DOI : 10.1016/S0167-2789(03)00153-2
Formation of singularities for wave equations including the nonlinear vibrating string, Communications on Pure and Applied Mathematics, vol.23, issue.3, pp.241-263, 1980. ,
DOI : 10.1002/cpa.3160330304
Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein???Gordon Equation, SIAM Journal on Numerical Analysis, vol.32, issue.6, pp.1839-1875, 1995. ,
DOI : 10.1137/0732083
A NON-STANDARD FINITE-DIFFERENCE SCHEME FOR CONSERVATIVE OSCILLATORS, Journal of Sound and Vibration, vol.240, issue.3, pp.587-591, 2001. ,
DOI : 10.1006/jsvi.2000.3167
A numerical integration technique for conservative oscillators combining nonstandard finite-difference methods with a Hamilton's principle, Journal of Sound and Vibration, vol.285, issue.1-2, pp.477-482, 2005. ,
DOI : 10.1016/j.jsv.2004.09.027
Theoretical Acoustics, 1968. ,
DOI : 10.1063/1.3035602
Backward Error Analysis for Numerical Integrators, SIAM Journal on Numerical Analysis, vol.36, issue.5, pp.1549-1570, 1999. ,
DOI : 10.1137/S0036142997329797
Symplectic integrators for Hamiltonian problems: an overview, Acta Numerica, vol.432, 1991. ,
DOI : 10.1016/0021-8928(84)90078-9
Numerical solution of a nonlinear Klein-Gordon equation, Journal of Computational Physics, vol.28, issue.2, pp.271-278, 1978. ,
DOI : 10.1016/0021-9991(78)90038-4
Global classical solutions for quasilinear hyperbolic systems, 1994. ,
Mécanique de la corde vibrante, 1993. ,
Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators, Physics Letters A, vol.133, issue.3, pp.134-139, 1988. ,
DOI : 10.1016/0375-9601(88)90773-6