VARIABLE TIME-STEP INTEGRATION WITH SYMPLECTIC METHODS

Symplectic methods for Hamiltonian systems are known to have favorable properties concerning long-time integrations (no secular terms in the error of the energy integral, linear error growth in the angle variab les instead of quadratic growth, comet qualitative behaviour) if they are applied with constant step sizes, while all of these properties ar e lost in a standard variable step size implementation. In this articl e we present a ''meta-algorithm'' which allows us to combine the use o f variable steps with symplectic integrators, without destroying the a bove mentioned favorable properties. We theoretically justify the algo rithm by a backward error analysis, and illustrate its performance by numerical experiments. (C) 1997 Elsevier Science B.V.