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Reversible long-term integration with variable step sizes
|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 methods — Extrapolation methods — Long-term integration — Hamiltonian problems — Reversible systems|