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Extrapolation of long-time symplectic integration
Robert Chan
chan@math.auckland.ac.nz
Department of Mathematics, The University of Auckland, New Zealand
joint work with Ander Murua (University of the Basque Country, Spain)We consider extrapolation as a way of improving the efficiency of symplectic integration over long time-intervals in a constant stepsize setting. Two modes are studied. In passive extrapolation, two sequences of approximations with stepsizes h and h/2 are obtained independently and combined whenever output is required. In active extrapolation, approximations with stepsizes h and h/2 are combined at every step and the extrapolated value is then propagated. Both modes are compared for the simple harmonic oscillator. The study of error growth of passive extrapolation over long time-intervals is extended to the periodic case and to integrable Hamiltonian systems where linear error growth has been established by Calvo and Hairer.
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