The life-span of backward error analysis for numerical integrators

Numerische Mathematik

Volumn 76, Issue 4, 1997, Pages 441-462

  Hairer, E ^a   Lubich, Ch ^b  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031505057     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050271     Document Type: Article

References (19)

1. Benettin, G., Giorgilli, A. (1994): On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms. J. Statist. Phys. 74, 1117-1143
2. Beyn, W.-J. (1987a): On the numerical approximation of phase portraits near stationary points. SIAM J. Numer. Anal. 24, 1095-1113
3. Beyn, W.-J. (1987b): On invariant closed curves for one-step methods. Numer. Math. 51, 103-122
4. Braun, M., Hershenov, J. (1977): Periodic solutions of finite difference equations. Quart. Appl. Maths. 35, 139-147
5. Butcher, J.C. (1987): The Numerical Analysis of Ordinary Differential Equations. Wiley, New York
6. Eirola, T. (1993): Aspects of backward error analysis of numerical ODE's. J. Comp. Appl. Math. 45, 65-73
7. Feng Kang (1991): Formal power series and numerical algorithms for dynamical systems. Proceedings of international conference on scientific computation, Hangzhou, China, Eds. Tony Chan and Zhong-Ci Shi, Series on Appl. Math. 1, 28-35
8. Fiedler, B., Scheurle, J. (1996): Discretization of homoclinic orbits, rapid forcing and "invisible" chaos. Mem. Amer. Math. Soc. 119, no. 570
9. Garay, B.M. (1993): Discretization and some qualitative properties of ordinary differential equations about equilibria. Acta Math. Univ. Comenian.. (N.S.) 62, 249-275
10. Hairer, E. (1994): Backward analysis of numerical integrators and symplectic methods. Annals of Numerical Mathematics 1, 107-132
11. Hairer, E., Nørsett, S.P., Wanner, G. (1993): Solving Ordinary Differential Equations I. Nonstiff Problems. Second Revised Edition. Springer Series in Computational Mathematics 8, Springer-Verlag
12. Perry, A.D., Wiggins, S. (1994): KAM tori are very sticky: rigorous lower bounds on the time to move away from an invariant Lagrangian torus with linear flow. Physica D 71, 102-121
13. Sanz-Serna, J.M. (1992): Symplectic integrators for Hamiltonian problems: an overview. Acta Numerica 1, 243-286
14. Sanz-Serna, J.M., Larsson, S. (1993): Shadows, chaos and saddles. Appl. Numer. Math. 13, 181-190
15. Stuart, A.M. (1994): Numerical analysis of dynamical systems. In: Iserles, A. (ed.) Acta Numerica 1994, 467-572. Cambridge University Press, Cambridge
16. Thirring, W. (1977): Lehrbuch der Mathematischen Physik 1. Klassische Dynamische Systeme. Springer-Verlag, Wien
17. Wiggins, S. (1990): Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer-Verlag, New York
18. Wilkinson, J.H. (1960): Error analysis of floating-point computation. Numer. Math. 2, 319-340
19. Yoshida, H. (1993): Recent progress in the theory and application of symplectic integrators. Celestial Mechanics and Dynamical Astronomy 56, 27-43