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Abstract: this article we study the influence of this truncation to the difference between the numerical solution and the exact solution of the perturbed differential equation. Results on the long-time behaviour of numerical solutions are obtained in this way. We present applications to the numerical phase portrait near hyperbolic equilibrium points, to asymptotically stable periodic orbits and Hopf bifurcation, and to energy conservation and approximation of invariant tori in Hamiltonian systems. (Update)
Context of citations to this paper: More
.... to exactly preserving the symplectic form, these integrators have been shown to conserve energy over exponentially long times [1, 7, 8, 26]. Such conservation properties are of crucial importance in celestial mechanics, molecular dynamics, and other application areas. As...
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BibTeX entry: (Update)
E. Hairer and Ch. Lubich. The life-span of backward error analysis for numerical integrators. Report, 1996. http://citeseer.ist.psu.edu/hairer96lifespan.html More
@article{ hairer97lifespan,
author = "E. Hairer and Ch. Lubich",
title = "The life-span of backward error analysis for numerical integrators",
journal = "Numerische Mathematik",
volume = "76",
number = "4",
pages = "441--462",
year = "1997",
url = "citeseer.ist.psu.edu/hairer96lifespan.html" }
Citations (may not include all citations):43 the Hamiltonian interpolation of near to the identity symple.. (context) - Benettin, Giorgilli - 1994
7 Formal power series and numerical algorithms for dynamical s.. (context) - Feng - 1991
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2 Solving Ordinary Differential Equations (context) - Numerical, Hairer et al. - 1993
2 KAM tori are very sticky: rigorous lower bounds on the time .. (context) - Problems, Edition et al. - 1994
2 The Numerical Analysis of Ordinary Differential Equations (context) - Maths, Butcher - 1987
2 chaos and saddles (context) - Numerica, Sanz-Serna et al. - 1993
2 Introduction to Applied Nonlinear Dynamical Systems and Chao.. (context) - Wien - 1990
2 Error analysis of floating-point computation (context) - New, Wilkinson - 1960
1 invisible (context) - international, scientific et al. - 1991
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