Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems

Abstract

We study the growth with time of (the coefficients of the asymptotic expansion of) the error in the numerical integration with linear multistep methods of periodic solutions of systems of ordinary differential equations. Particular attention is devoted to reversible systems. It turns out that symmetric linear multistep methods cannot be recommended in spite of the fact that they mimic the reversibility of the true flow. For reversible second-order systems, linear multistep methods without parasitic double roots are useful.