Runge-Kutta methods for orthogonal and isospectral flows

Applied Numerical Mathematics

Volumn 22, Issue 1-3 SPEC. ISS., 1996, Pages 153-163

  Calvo, M P ^a   Iserles, A ^b   Zanna, A ^c  

^a UNIVERSITY OF VALLADOLID   (Spain)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c NEWNHAM COLLEGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; GEOMETRY; MATRIX ALGEBRA;

ISOSPECTRAL FLOWS; ORTHOGONAL FLOWS; RUNGE KUTTA METHODS;

NUMERICAL METHODS;

EID: 0030286081     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0168-9274(96)00029-3     Document Type: Article

References (18)

1. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations (Wiley, Chichester, 1987).
2. M.P. Calvo, A. Iserles and A. Zanna, Numerical solution of isospectral flows, DAMTP Technical Report 1995/NA03, University of Cambridge (1995).
3. M.P. Calvo, A. Iserles and A. Zanna, Semi-explicit methods for isospectral flows, in preparation.
4. M.P. Calvo, A. Iserles and A. Zanna, Conservative methods for the Toda lattice equations, in preparation.
5. M.P. Calvo, A. Iserles and A. Zanna, Numerical methods on differentiable manifolds, in preparation.
6. M.T. Chu, A list of matrix flows with applications, in: A. Bloch, ed., Hamiltonian and Gradients Flows, Algorithms and Control, Fields Institute Communications (American Mathematical Society, Providence, RI, 1994) 87-97.
7. G.J. Cooper, Stability of Runge-Kutta methods for trajectory problems, IMA J. Numer. Anal. 7 (1987) 1-13.
8. L. Dicci, R.D. Russell and E.S. van Vleck, Unitary integrators and applications to continuous orthonormalization techniques, SIAM J. Numer. Anal. 31 (1994) 261-281.
9. A.T. Fomenko, Symplectic Geometry (Gordon and Breach, New York, 1988).
10. E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, Berlin, 2nd ed., 1993).
11. R.A. Horn and C.R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1986).
12. A. Iserles, A First Course in the Numerical Analysis of Differential Equations (Cambridge University Press, Cambridge, 1996).
13. A. Iserles and A. Zanna, Qualitative numerical analysis of ordinary differential equations, DAMTP Technical Report 1995/NA5; in: J. Renegar, M. Shub and S. Smale, eds., Lectures in Applied Mathematics (American Mathematical Society, Providence, RI, to appear).
14. P.J. Olver, Applications of Lie Groups to Differential Equations (Springer, New York, 2nd ed., 1991).
15. A.M. Perelomov, Integrable Systems of Classical Mechanics and Lie Algebras, Vol. 1 (Birkhäuser, Basel, 1990).
16. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems (Chapman and Hall, London, 1994).
17. M. Toda, Theory of Nonlinear Lattices (Springer, Berlin, 1981).
18. D.S. Watkins, Isospectral flows, SIAM Rev. 26 (1984) 379-391.