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Preserving first integrals with symmetric Lie group methods

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  • The discrete gradient approach is generalized to yield first integral preserving methods for differential equations in Lie groups.
    Mathematics Subject Classification: Primary: 65L05, 65P10; Secondary: 22E70.


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  • [1]

    R. L. Adler, J. P. Dedieu, J. Y. Margulies, M. Martens and M. Shub, Newton's method on Riemannian manifolds and a geometric model for the human spine, IMA Journal of Numerical Analysis, 22 (2002), 359-390.doi: 10.1093/imanum/22.3.359.


    Luigi Brugnano, Felice Iavernaro and Donato Trigiante., Hamiltonian boundary value methods (energy preserving discrete line integral methods), JNAIAM. J. Numer. Anal. Ind. Appl. Math., 5 (2010), 17-37.


    E. Celledoni, V. Grimm, R. I. McLachlan, D. I. McLaren, D. O'Neale, B. Owren and G. R. W. Quispel, Preserving energy resp. dissipation in numerical pdes using the "average vector field" method, Journal of Computational Physics, 231 (2012), 6770-6789.doi: 10.1016/j.jcp.2012.06.022.


    E. Celledoni, H. Marthinsen and B. Owren, An introduction to Lie group integrators - basics, new developments and applications, Journal of Computational Physics, (2013). To appear.doi: 10.1016/j.jcp.2012.12.031.


    S. H. Christiansen, H. Z. Munthe-Kaas and B. Owren, Topics in structure-preserving discretization, Acta Numerica, 20 (2011), 1-119.doi: 10.1017/S096249291100002X.


    David Cohen and Ernst Hairer, Linear energy-preserving integrators for Poisson systems, BIT, 51 (2011), 91-101.doi: 10.1007/s10543-011-0310-z.


    M. Dahlby and B. Owren, A general framework for deriving integral preserving numerical methods for PDEs, SIAM J. Sci. Comput., 33 (2011), 2318-2340.doi: 10.1137/100810174.


    O. Gonzalez, Time integration and discrete Hamiltonian systems, J. Nonlinear Sci., 6 (1996), 449-467.doi: 10.1007/BF02440162.


    E. Hairer, Energy-preserving variant of collocation methods, Journal of Numerical Analysis, Industrial and Applied Mathematics, 5 (2010), 73-84.


    A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett and A. Zanna, Lie-group methods, Acta Numerica, 9 (2000), 215-365.doi: 10.1017/S0962492900002154.


    D. Lewis and J. C. Simo, Nonlinear stability of rotating pseudo-rigid bodies, Proc. R. Soc. Lond. A, 427 (1990), 281-319.doi: 10.1098/rspa.1990.0014.


    D. Lewis and J. C. Simo, Conserving algorithms for the dynamics of Hamiltonian systems of Lie groups, J. Nonlinear Sci., 4 (1994), 253-299.doi: 10.1007/BF02430634.


    R. I. McLachlan, G. R. W. Quispel and N. Robidoux, Geometric integration using discrete gradients, Phil. Trans. Royal Soc. A, 357 (1999), 1021-1045.doi: 10.1098/rsta.1999.0363.


    A. Zanna, Collocation and relaxed collocation for the Fer and the Magnus expansions, SIAM J. Numer. Anal., 36 (1999), 1145-1182.doi: 10.1137/S0036142997326616.

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