Reversible Long-Term Integration with Variable Stepsizes
- 1 January 1997
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 18 (1) , 257-269
- https://doi.org/10.1137/s1064827595285494
Abstract
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).Keywords
This publication has 11 references indexed in Scilit:
- Accurate long-term integration of dynamical systemsApplied Numerical Mathematics, 1995
- Building a better leapfrogThe Astrophysical Journal, 1995
- Variable steps for reversible integration methodsComputing, 1995
- On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithmsJournal of Statistical Physics, 1994
- Numerical Hamiltonian ProblemsPublished by Springer Nature ,1994
- Invariant curves for variable step size integratorsBIT Numerical Mathematics, 1992
- Solving Ordinary Differential Equations IIPublished by Springer Nature ,1991
- Integrable Systems of Classical Mechanics and Lie AlgebrasPublished by Springer Nature ,1990
- On the sharpness of theorems concerning zero-free regions for certain sequences of polynomialsNumerische Mathematik, 1976
- The equivalence of von Zeipel mappings and Lie transformsCelestial Mechanics and Dynamical Astronomy, 1970