Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems

IMA Journal of Numerical Analysis

Volumn 18, Issue 1, 1998, Pages 57-75

  Cano, B ^a   Sanz Serna, J M ^a  

^a UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ORDINARY DIFFERENTIAL EQUATIONS;

ASYMPTOTIC EXPANSION; LINEAR MULTISTEP METHOD; MULTI STEP METHODS; NUMERICAL INTEGRATIONS; REVERSIBLE SYSTEMS; SECOND-ORDER SYSTEMSS; SYMMETRIC LINEAR MULTISTEP METHODS; SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS;

NUMERICAL METHODS;

EID: 0032372573     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/18.1.57     Document Type: Article

References (19)

1. ARNOLD, V. I., & SEVRYUK, M. B. 1986 Oscillations and bifurcations in reversible systems. Non-linear Phenomena in Plasma Physics and Hydrodynamics (R. Z. Sageev, ed). Moscow: Mir, pp 31-64.
2. CALVO, M. P., & HAIRER, E. 1995 Accurate long-term integration of dynamical systems. Appl. Numer. Math. 18, 95-105.
3. CALVO, M. P., & SANZ-SERNA, J. M. 1993 The development of variable-step symplectic integrators, with application to the two-body problem. SIAM J. Sci. Comput. 14, 936-952.
4. CANO, B. 1996 Integración mumérica de orbitas periódicas con métodos multipaso. PhD Thesis, Universidad de Valladolid.
5. CANO, B., & SANZ-SERNA, J. M. 1995 Error growth in the numerical integration of periodic orbits, with application to Hamiltonian and reversible systems. SIAM J. Numer. Anal. To appear.
6. EIROLA, T., & SANZ-SERNA, J. M. 1991 Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods. Numer. Math. 61, 281-290.
7. ESTEP, D. J., & STUART, A. M. 1995 The rate of error growth in Hamiltonian-conserving integrators. Z. Angew. Math. Phys. 46, 407-418.
8. FRUTOS, J. DE, & SANZ-SERNA, J. M. 1997 Accuracy and conservation properties in numerical integration: the case of the Korteweg-de Vries equation. Numer. Math. 75, 421-445.
9. HAIRER, E., NØRSETT, S. P., & WANNER, W. G. 1993 Solving Ordinary Differential Equations I, Nonstiff Problems 2nd edn. Berlin: Springer.
10. HAIRER, E., & STOFFER, D. 1997 Reversible long-term integration with variable step sizes. SIAM J. Sci. Comput. 18, 257-269.
11. PORTILLO, A., & SANZ-SERNA, J. M. 1995 Lack of dissipativity is not symplecticness. BIT 35, 269-276.
12. QUINLAN, G. D., & TREMAINE, S. 1990 Symmetric multistep methods for the numerical integration of planetary orbits. Astron. J. 100, 1694-1700.
13. SANZ-SERNA, J. M. 1997 Geometric integration. The State of the Art in Numerical Analysis. (I. S. Duff and G. A. Watson, eds). Oxford: Clarendon, pp 121-143.
14. SANZ-SERNA, J. M., & CALVO, M. P. 1994 Numerical Hamiltonian Problems. London: Chapman & Hall.
15. SEVRYUK, M. B. 1986 Reversible Systems (Springer Lecture Notes in Mathematics 1211). Berlin: Springer.
16. STETTER, H. J. 1970 Symmetric two-step algorithms for ordinary differential equations. Computing 5, 267-280.
17. STETTER, H. J. 1973 Analysis of Discretization Methods for Ordinary Differential Equations. Berlin: Springer.
18. STOFFER, D. 1988 On reversible and canonical integration methods. Research Report 88-05, Applied Mathematics Department, Eidgenössische Technische Hochschule (ETH) Zürich.
19. STOFFER, D. 1995 Variable steps for reversible integration methods. Computing 55, 1-22.