ABSTRACT
This chapter describes a simple approach to the application of a variable coefficient procedure which is closely related to the Adams methods. In the starting phase of integration, the advantages of the variable coefficient formulae over Adams formulae are very clear. Since the step-size can be changed from step to step without forming explicit interpolants, the increase in step-size appropriate to a gain in order can be accommodated. Since the order as well as the step-size can be varied with the method derived, it is possible to start the solution of an initial value problem with a first order formula if a small-enough steplength is specified. The choice of this initial steplength is important. For their STEP integrator code, Shampine and Gordon adopted an approach in which were defined modified divided differences, reducing to backward differences for constant steplengths.
