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Explicit, time reversible, adaptive step size control

Soederlind, Gustaf
Published in SIAM Journal on Scientific Computing. 2005, vol. 26, no. 6, p. 1838-1851
Abstract Adaptive step size control is difficult to combine with geometric numerical integration. As classical step size control is based on ``past'' information only, time symmetry is destroyed and with it also the qualitative properties of the method. In this paper we develop completely explicit, reversible and symmetry preserving, adaptive step size selection algorithms for geometric numerical integrators such as the St"ormer--Verlet method. A new step density controller is proposed and analyzed using backward error analysis and reversible perturbation theory. For integrable reversible systems we show that the resulting adaptive method nearly preserves all action variables and, in particular, the total energy for Hamiltonian systems. It has the same excellent long term behaviour as if constant steps were used. With variable steps, however, both accuracy and efficiency are greatly improved.
Keywords Adaptive integrationGeometric integrationTime reversible and symmetric methodsStörmer--Verlet methodHamiltonian systemsExplicit and reversible step size controlBackward error analysisReversible perturbation theory
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HAIRER, Ernst, SOEDERLIND, Gustaf. Explicit, time reversible, adaptive step size control. In: SIAM Journal on Scientific Computing, 2005, vol. 26, n° 6, p. 1838-1851. https://archive-ouverte.unige.ch/unige:12120

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Deposited on : 2010-10-15

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