Keywords: Stiff problems, A-stability, stability barriers, order stars, order arrows, nonlinear
stability.

Abstract: 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.

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