On variable coefficient multistep methods

In this monograph, we develop a subclass of variable coefficient multistep (VCM) methods, which is A-contractive. -- We introduce a set of simplifying conditions to relate VCM methods to the Padé approximants of the exponential function exp(z). We then proceed with the construction of the arbitrary order, A-contractive, variable stepsize VCM methods. Both linearly implicit and fully implicit families are considered. -- The convergence properties of VCM methods are discussed in chapter 3. We show the stiff-independent convergence for VCM methods on general nonlinear dissipative problems. We also demonstrate convergence of VCM methods when applied to singular perturbation problems with the convergence being independent of the perturbation parameter. -- Finally, in chapter 4 we report on a set of numerical experiments with fourth and fifth order linearly implicit and fully implicit methods