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Reversible long-term integration with variable stepsizes
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DOI：10.1137/S1064827595285494.png)
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摘要
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The numerical integration of reversible dynamical systems is considered. A backward analysis for variable stepsize one-step methods is developed, and it is shown that the numerical solution of a symmetric one-step method, implemented with a reversible stepsize 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 nonsymmetric integrators (quadratic error growth).
Keyword:
symmetric Runge-Kutta methods
extrapolation methods
long-term integration
Hamiltonian problems
reversible systems
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