A multi-purpose system for the numerical integration of ODE's

摘要

In this paper we describe the development of an experimental multi-purpose integration system. Strongly modular, the system allows the use of wide classes of multistep methods for solving ODE's, singulsr perturbation problems as well as implicit differential-algebraic equations.We focus our attention on a new family of collocation methods for nonstiff problems. While these methods are strongly related to the stiffly stable BDF methods, they are particularly well suited for the implementation of a “type-insensitive” integration algorithm. Compound discretizations, in which certain variables are integrated with the first method and others with the second, can also be used. A stability analysis is given, and some implementation issues are discussed.