Variable multistep methods for delay differential equations

Abstract

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.