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Abstract: We survey briefly recent developments in geometric integration and numerical methods on manifolds. The underlying philosophy is that numerical methods should, whenever practicable, recover correctly known qualitative behaviour of the underlying differential system. Classical numerical methods retain invariants very poorly indeed, and this justifies the recent introduction of a new breed of discretization schemes. (Update)
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BibTeX entry: (Update)
@misc{ -unknown,
title = "Unknown",
url = "citeseer.ist.psu.edu/676615.html" }
Citations (may not include all citations):235 Classical Mechanics (context) - Goldstein - 1978
59 Dynamical Systems and Numerical Analysis (context) - Stuart, Humphries - 1996
55 the exponential solution of differential equations for a lin.. (context) - Magnus - 1954
52 Numerical Hamiltonian Problems (context) - Sanz-Serna, Calvo - 1994
50 Theory of Nonlinear Lattices (context) - Toda - 1981
39 the solution of linear differential equations in Lie groups - Iserles, Nrsett - 1997
39 Numerical integration of ordinary differential equations on .. (context) - Crouch, Grossman - 1993
34 Numerical Methods for Scientists and Engineers (context) - Hamming - 1962
25 Numerical solution of isospectral flows - Calvo, Iserles et al. - 1997
17 Runge--Kutta methods on Lie groups (context) - Munthe-Kaas - 1997
14 Numerical methods (context) - Iserles - 1997
13 Reversible adaptive regularization I: Perturbed Kepler motio.. - Leimkuhler - 1997
13 A list of matrix flows with applications - Chu - 1994
8 Numerical integration of differential equations on homogeneo.. (context) - Munthe-Kaas, Zanna - 1997
6 Equivalence, Invariants and Symmetry (context) - Olver - 1995
6 Numerical methods on differentiable manifolds (context) - Calvo, Iserles et al. - 1997
4 Integration methods for molecular dynamics - Leimkuhler, Reich et al. - 1996
3 Runge--Kutta methods for orthogonal and isospectral flows (context) - Calvo, Iserles et al. - 1996
1 Integration Algorithms for Classical Mechanics (context) - Marsden, Patrick et al. - 1996
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