Ordinary differential equations

Abstract

These days everyone talks about “impact” as something that can be measured in terms of citations within a year or two, but the impact of many important contributions to science can be looked at in other, more perceptive, ways. I believe this is especially true of [GA14]. This paper is forward-looking to the extent that its importance has become recognised more and more as time has passed. In my opinion the impact of this contribution has been tremendous. Over the years it has become known as a pioneering paper in the fitted type of approach to the solution of initial value problems. It has been referenced directly soon after its publication but even more so in recent years. It is related to exponential integration, to exponential fitting, and to modern approaches to the solution of highly-oscillatory problems. The ideas and results in the original paper have been rediscovered independently by later authors, but the depth and scholarship in Gautschi’s exposition are unmatched. Here are the key definitions near the start of the paper.