The development of a multipurpose integration system is described. The intention is to allow the use of different classes of methods for solving ordinary differential equations, singular perturbation problems as well as implicit differential-algebraic equations. The environment provided is intended to facilitate the testing of new ideas and the comparison of different strategies associated with the implementation of such methods.
To illustrate the system the implementation of a new family of methods for non-stiff problems, obtained by adding a difference correction to the backward differential formula (BDF) methods, is outlined. The methods have larger stability regions but bigger error constants than the Adams methods. They facilitate the implementation of a type-intensitive code since it is relatively easy to switch between these and the BDF methods. Detecting stiffness and switching criteria are considered. Compound discretizations, for a partitioned form of the problem are also considered in the context of these methods and a stability analysis based on contractivity is discussed.