Variable multistep methods for delay differential equations

In this paper, variable stepsize multistep methods for delay differential equations of the type y(t) = f(t, y(t), y(t − τ)) are proposed. Error bounds for the global discretization error of variable stepsize multistep methods for delay differential equations are explicitly computed. It is proved that a variable multistep method which is a perturbation of strongly stable fixed step size method is convergent.