Forty-Five Years of A-stability

We discuss two events with profound implications on the way initial value problems are solved numerically. The first was the identification of stiffness as a widely spread phenomenon affecting the ability to obtain useful results. The second was the definition of A-stability as an important approach to overcoming the effect of stiffness. Not only was the idea associated with A-stability significant in its own time but it has had long term effects including new theoretical questions as well as the tools for solving them. c © 2009 European Society of Computational Methods in Sciences and Engineering