Extensions of a New Algorithm for the Numerical Solution of Linear Differential Systems on an Infinite Interval

on an interval [X,∞). Here Z is an n-component vector, ρ is a scalar factor, D is a constant diagonal matrix and R is a perturbation matrix such that R(x) = O(x) as x → ∞, for some δ > 0. The algorithm implements a repeated transformation process by means of which ( 1. 1) is transformed into other systems whose perturbation matrices are of successively smaller orders of magnitude as x → ∞. When the perturbation reaches a prescribed accuracy, the Levinson asymptotic theorem [5],[4] provides the solution of the final system in the process, the solution also possessing that accuracy. The corresponding solution of (1. 1) is then obtained by transforming back. The algorithm has two main aspects. The first is the algebraic one of generating symbolically the matrix terms which appear in the transformation process. In [2] and [1], the algorithm was set up in such a way that this aspect is implemented in the symbolic algebra system Mathematica. The other aspect