Energy-preserving variant of collocation methods

Journal of Numerical Analysis, Industrial and Applied Mathematics

Volumn 5, Issue 1-2, 2010, Pages 73-84

  Hairer, E ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

B series; Collocation; Conjugate symplecticity; Energy preserving integrators; Gaussian quadrature; Hamiltonian systems; Runge Kutta methods; Symmetry

Indexed keywords

EID: 79251639390     PISSN: 17908140     EISSN: 17908159     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

1. L. Brugnano, F. Iavernaro, and D. Trigiante. Analysis of Hamiltonian boundary value methods (HBVMs) for the numerical solution of polynomial Hamiltonian dynamical systems. Submitted for publication, 2009.
2. E. Celledoni, R. I. McLachlan, D. I. McLaren, B. Owren, G. R.W. Quispel, andW. M.Wright. Energy-preserving Runge-Kutta methods. M2AN Math. Model. Numer. Anal., 43(4):645-649, 2009.
3. E. Celledoni, R. I. McLachlan, B. Owren, and G. R.W. Quispel. Energy-preserving integrators and the structure of B-series. NTNU Report No. 5, 2009.
4. P. Chartier, E. Hairer, and G. Vilmart. Algebraic structures of B-series. To appear in Foundations of Comput. Math., 2010.
5. E. Faou, E. Hairer, and T.-L. Pham. Energy conservation with non-symplectic methods: examples and counter-examples. BIT, 44:699-709, 2004.
6. E. Hairer, C. Lubich, and G. Wanner. Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics 31. Springer-Verlag, Berlin, 2nd edition, 2006.
7. E. Hairer, S. P. Nørsett, and G. Wanner. Solving Ordinary Differential Equations I. Nonstiff Problems. Springer Series in Computational Mathematics 8. Springer, Berlin, 2nd edition, 1993.
8. E. Hairer and G. Söderlind. Explicit, time reversible, adaptive step size control. SIAM J. Sci. Comput., 26:1838-1851, 2005.
9. F. Iavernaro and D. Trigiante. High-order symmetric schemes for the energy conservation of polynomial Hamiltonian problems. JNAIAM J. Numer. Anal. Ind. Appl. Math., 4(1-2):87- 101, 2009.
10. G. R. W. Quispel and D. I. McLaren. A new class of energy-preserving numerical integration methods. J. Phys. A, 41(4):045206, 7, 2008.