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Scientific article
English

Reversible long-term integration with variable step sizes

Published inSIAM journal on scientific computing, vol. 18, no. 1, p. 257-269
Publication date1997
Abstract

The numerical integration of reversible dynamical systems is considered. A backward analysis for variable step size one-step methods is developed and it is shown that the numerical solution of a symmetric one-step method, implemented with a reversible step size strategy, is formally equal to the exact solution of a perturbed differential equation, which again is reversible. This explains geometrical properties of the numerical flow, such as the nearby preservation of invariants. In a second part, the efficiency of symmetric implicit Runge-Kutta methods (linear error growth when applied to integrable systems) is compared with explicit non-symmetric integrators (quadratic error growth).

Keywords
  • Symmetric Runge-Kutta methods
  • Extrapolation methods
  • Long-term integration
  • Hamiltonian problems
  • Reversible systems
Citation (ISO format)
HAIRER, Ernst, STOFFER, Daniel. Reversible long-term integration with variable step sizes. In: SIAM journal on scientific computing, 1997, vol. 18, n° 1, p. 257–269.
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Article (Published version)
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Identifiers
  • PID : unige:12435
ISSN of the journal1064-8275
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