| Description: |
The numerical integration of reversible dynamicalsystems 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). Key words. symmetric Runge-Kutta methods, extrapolation methods, long-term integration, Hamiltonian problems, reversible systems AMS subject classifications. 65L05, 34C35 1. Introduction. We consider the numerical treatment of systems (1.1) y 0 = f(y); y(0) = y0 ; where the evolution of dynamical . |
