ETHZ Research Project

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Variable Step Size Integration for Reversible Systems

Conventional variable step implementation of symplectic or reversible integration methods destroy the symplectic or reversible structure of the system. In fact we prove that the symplectic structure is preserved only if the step size is essentially kept constant. For reversible methods however variable step sizes are feasible provided the following symmetry condition is satisfied: the step-size is the same for ``reflected'' steps. We construct reversible variable step size schemes based on explicit integrators. Numerical experiments show that for Kepler's problem the new methods perform better than conventional variable step size procedures or symplectic schemes with constant step size. In particular they exhibit linear growth of the global error (as do symplectic methods with constant step size). For details see D. Stoffer, ''Variable steps for reversible integration methods''; Computing 55, 1-22 (1995).
Implementation of reversible step size algorithms for implicit Runge-Kutta methods and backward analysis of variable step size methods were studied in collaboration with Ernst Hairer, see : E. Hairer, D. Stoffer, Reversible long-term integration with variable step sizes, SIAM J. Sci. Comput., 18, 257-269 (1997).

Contacts:

PD Dr. D. Stoffer

Electronic Contacts:

stoffer@math.ethz.ch

In Collaboration With:

E. Hairer

Last Update:

04/07/97

Responsible:

Professor or Project Leader:           : Prof. Dr. Urs Kirchgraber
Institute or Independent Professorship : Independent Professorship of Mathematics
Department                             : Department of Mathematics

Comments to the ETH Research Report administration : Sat Jun 19 16:30:35 1999

© 2001 by ETH Zurich | last change: October 30, 2001 | webmaster
author Michele Marcionelli and design: Michele Marcionelli