Multistep methods are classically constructed by specially
designed difference operators on an equidistant time grid. To make
them practically useful, they have to be implemented by varying
the step-size according to some error-control algorithm. It is
well known how to extend Adams and BDF formulas to a variable
step-size formulation. In this paper we present a collocation
approach to construct variable step-size formulas for a wider
class of multistep methods including methods like DCBDF and IDC
methods. We make use of piecewise polynomials to show that every
-step method of order 
has a variable step-size polynomial
collocation formulation.