Variable multistep methods for higher-order delay differential equations

In this paper, variable stepsize multistep methods for higher-order delay differential equations of the type y(r)(t) = f(t, y(t), y(t−τ)) are proposed. Explicit error bounds for the global discretization error are given. It is proved that a variable multistep method which is a perturbation of strongly stable fixed stepsize method is convergent.