On the long time error of first integrals for some RK numerical integrators

Journal of Numerical Analysis, Industrial and Applied Mathematics

Volumn 4, Issue 1-2, 2009, Pages 77-86

  Calvo, M ^a   Montijano, J I ^a   Laburta, M P ^a   Randez L ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Geometric integration; Invariant preservation; Runge Kutta methods

Indexed keywords

EID: 67650688595     PISSN: 17908140     EISSN: 17908159     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (8)

1. A. Aubry and P. Chartier, Pseudo-Symplectic Runge-Kutta methods, BIT, 98, No 3, 439-461 (1998).
2. M. Calvo, M.P. Laburta, J.I. Montijano and L. Rández, Error growth in the numerical integration of periodic orbits, Technical report, Dept. de Matemática aplicada, Univ. de Zaragoza (2008).
3. B. Cano, J.M. Sanz-Serna, Error Growth in the Numerical Integration of Periodic Orbits, with Application to Hamiltonian and Reversible Systems, SIAM J. Numer. Anal., 34, No 4, 1391-1417 (1997).
4. C. M. Field and F. W. Nijhoff, A note on modified Hamiltonians for numerical integrations admitting an exact invariant, Nonlinearity, 16, 1673-1683 (2003).
5. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration: Structure Preserving algorithms for Ordinary Differential Equations, Second edition, Springer Verlag, Berlin, 2006.
6. L.F. Shampine and M. W. Reichelt, The MATLAB ODE suite, SIAM J. Sci. Comput., 18, 1, 1-22 (1997).
7. Yu. B. Suris, Integrable mappings of the standard type, Funct. Anal. Appl., 23, 74-76 (1989).
8. A.P. Veselov, Integrable maps, Russ. Math. Surv., 46, 1-51 (1991).