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Reversible long-term integration with variable step sizes

Stoffer, Daniel
Published in SIAM Journal on Scientific Computing. 1997, vol. 18, no. 1, p. 257-269
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 methodsExtrapolation methodsLong-term integrationHamiltonian problemsReversible systems
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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. https://archive-ouverte.unige.ch/unige:12435

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Deposited on : 2010-11-12

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