On the efficient and reliable numerical solution of large linear systems of O.D.E.'s

Using a Combination of numerical techniques from linear algebra and from ordinary differential equations, a package of efficient procedures are described for the efficient numerical solution of large linear systems of O.D.E.'s. The techniques avoid the explicit approximation of the matrix exponential and exploit any structure that is inherent in the system. Numerical results are presented which illustrate the gain in efficiency that is possible.