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Abstract: One of the most fruitful ways to analyze the effects of discretization error in the numerical solution of a system of differential equations is to examine the "modified equations," which are the equations that are exactly satisfied by the (approximate) discrete solution. These do not actually exist in general, but rather are defined by an asymptotic expansion in powers of the discretization parameter. Nonetheless, if the expansion is suitably truncated, the resulting modified equations have a... (Update)
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BibTeX entry: (Update)
R. D. Skeel and D. J. Hardy. Practical construction of modified Hamiltonians. SIAM J. on Sci. Comput., 23(4):1172--1188, November 2001. http://citeseer.ist.psu.edu/skeel01practical.html More
@article{ skeel02practical,
author = "Robert D. Skeel and David J. Hardy",
title = "Practical Construction of Modified {Hamiltonians}",
journal = "SIAM Journal on Scientific Computing",
volume = "23",
number = "4",
pages = "1172--1188",
year = "2002",
url = "citeseer.ist.psu.edu/skeel01practical.html" }
Citations (may not include all citations):77 Numerical Hamiltonian Problems (context) - Sanz-Serna, Calvo - 1994
43 the Hamiltonian interpolation of near to the identity symple.. (context) - Benettin, Giorgilli - 1994
38 The life-span of backward error analysis for numerical integ.. - Hairer, Lubich - 1997
33 Backward error analysis for numerical integrators - Reich ACM
25 NAMD2: Greater scalability for parallel molecular dynamics - Kal'e, Skeel et al. - 1999
20 Generalized Verlet algorithm for efficient molecular dynamic.. (context) - Grubmuller, Heller et al. - 1991
18 Molecular Modelling: Principles and Applications (context) - Leach - 1996
17 Longer time steps for molecular dynamics (context) - Izaguirre, Reich et al. - 1999
17 object-oriented molecular dynamics program (context) - Nelson, Humphrey et al. - 1996
17 The modified equation approach to the stability and accuracy.. (context) - Warming, Hyett - 1974
14 Nonlinear resonance artifacts in molecular dynamics simulati.. (context) - Schlick, Mandziuk et al. - 1998
14 the scope of the method of modified equations (context) - Griffiths, Sanz-Serna - 1986
9 Integration schemes for molecular dynamics and related appli.. (context) - Skeel - 1999
7 An analysis of the accuracy of Langevin and molecular dynami.. (context) - Pastor, Brooks et al. - 1988
7 Asymptotic expansions and backward analysis for numerical in.. - Hairer, Lubich - 2000
6 Long-time-step methods for oscillatory differential equation.. - Garc'ia-Archilla, Sanz-Serna et al. - 1998 ACM
5 Some Geometric and Numerical Methods for Perturbed Integrabl.. (context) - Stoffer - 1988
3 A numerical algorithm for Hamiltonian systems (context) - Rowlands - 1991 ACM
1 Common molecular dynamics algorithms revisited: Accuracy and.. (context) - Mazur - 1997
1 Residual acceleration as a measure of the accuracy of molecu.. (context) - Gans, Chan et al. - 1999
1 Shadow mass and the relationship between velocity and moment.. (context) - Gans, Shalloway - 2000
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