Cost efficient lie group integrators in the RKMK class

BIT Numerical Mathematics

Volumn 43, Issue 4, 2003, Pages 723-742

  Casas, F ^a   Owren, B ^b,c  

^a UNIVERSITAT JAUME I   (Spain)

^b NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^c Centre for Advanced Studies   (Norway)

Author keywords

Geometric integration; Lie algebras; Lie groups; Numerical analysis; Numerical integration of ordinary differential equations on manifolds; Time integration

Indexed keywords

EID: 4043073404     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:BITN.0000009959.29287.d4     Document Type: Article

References (10)

1. S. Blanes and F. Casas, Optimization of Lie group methods for differential equations, Future Generation Computer Systems, 19 (2003), pp. 331-339.
2. S. Blanes, F. Casas, and J. Ros, High order optimized geometric integrators for linear differential equations, BIT, 42(2) (2002), pp. 262-284.
3. J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations, Wiley, Chichester, 1987.
4. F. Casas and B. Owren, Cost efficient Lie group integrators in the RKMK class, Technical Report Numerics no.5/2002, Norwegian University of Science and Technology, Trondheim, Norway, 2002.
5. E. Celledoni, A. Iserles, S. P. Nørsett, and B. Orel, Complexity theory for Lie-group solvers, J. Complexity, 18(1) (2002), pp. 242-286.
6. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, Springer-Verlag, 2nd revised ed., 1993.
7. A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, and A. Zanna, Lie-group methods, Acta Numerica, 9 (2000), pp. 215-365.
8. A. Iserles and S. P. Nørsett, On the solution of linear differential equations in Lie groups, Phil. Trans. Royal Soc. A, 357 (1999), pp. 983-1020.
9. H. Munthe-Kaas, High order Runge-Kutta methods on manifolds, Appl. Numer. Math., 29 (1999), pp. 115-127.
10. H. Munthe-Kaas and B. Owren, Computations in a free Lie algebra, Phil. Trans. Royal Soc. A, 357 (1999), pp. 957-981.