Approximately preserving symmetries in the numerical integration of ordinary differential equations

European Journal of Applied Mathematics

Volumn 10, Issue 5, 1999, Pages 419-445

  Iserles, Arieh ^a   McLachlan, Robert ^b   Zanna, Antonella ^c  

^a Department of Applied Mathematics ^*  (United Kingdom)

^b MASSEY UNIVERSITY   (New Zealand)

^c NEWNHAM COLLEGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033446079     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792599003927     Document Type: Article

References (20)

1. ABLOWITZ, M. J. & CLARKSON, P. A. (1991) Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Mathematical Society Lecture Note Series, Vol. 149. Cambridge University Press.
2. CALVO, M. P., ISERLES, A. & ZANNA, A. (1996) 'Runge - Kutta methods for orthogonal and isospectral flows ', Appl. Num. Maths 22, 153-163.
3. CALVO, M. P., ISERLES, A. & ZANNA, A. (1997a) 'Numerical solution of isospectral flows', Maths Comput. 66, 1461-1486.
4. CALVO, M. P., ISERLES, A. & ZANNA, A. (1997b) Semi-explicit methods for isospectral flows, Technical Report 1997/NA16, University of Cambridge.
5. CARTER, R., SEGAL, G. & MACDONALD, I. (1995) Lectures on Lie groups and Lie algebras, London Mathematical Society Student Texts, Vol. 32. Cambridge University Press.
6. CHU, M. T. (1994) A list of matrix flows with applications. In: A. Bloch (ed.) Hamiltonian and Gradient Flows, Fields Institute Communications, American Mathematics Society, Providence, RI, pp. 87-97.
7. DIECI, L., RUSSELL, R. D. & VAN VLECK, E. S. (1994) Unitary integrators and applications to continuous orthonormalization techniques, SIAM J. Numer. Anal. 31, 261-281.
8. FRANK, J., HUANG, W. & LEIMKUHLER, B. (1997) Geometric integrators for classical spin systems. J. Comput. Phys. 133(1), 160-172.
9. HAIRER, E. & WANNER, G. (1991) Solving Ordinary Differential Equations II: Stiff Problems and Differential-Algebraic Equations, Springer-Verlag.
10. ISERLES, A. (1997) Beyond the classical theory of computational ordinary differential equations. In: I. Duff & G. Watson (eds.), State of the Art in Numerical Analysis, Oxford University Press, pp. 171-192.
11. LOTHAIRE, M. (1983) Combinatorics on Words, Addison-Wesley.
12. MCLACHLAN, R. I. (1995) On the numerical integration of ordinary differential equations by symmetric composition methods. SIAM J. Sci. Comp. 16, 151-168.
13. MCLACHLAN, R. I., QUISPEL, G. R. W. & TURNER, G. S. (1997) Numerical integrators that preserve symmetries and reversing symmetries. SIAM J. Numer. Anal. to appear.
14. OLVER, P. J. (1995) Equivalence, Invariants, and Symmetry, Cambridge University Press.
15. REICH, S. (1997) Dynamical systems, numerical integration, and exponentially small estimates. Habilitationsschrift, Free University of Berlin.
16. STRANG, G. (1964) Accurate partial difference methods ii: nonlinear problems. Numer. Math. 6, 37.
17. STUART, A. M. & HUMPHRIES, A. R. (1996) Dynamical Systems and Numerical Analysis, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press.
18. SUZUKI, M. (1990) Fractal decomposition of exponential operators with applications to many-body theories and Monte-Carlo simulations. Phys. Letters A 146, 319-323.
19. TODA, M. (1981) Theory of Nonlinear Lattices, Springer-Verlag.
20. YOSHIDA, H. (1990) Construction of higher order symplectic integrators. Phys. Letters A 150, 262-268.