The authors present a two-parameter family of test problems for ordinary differential equations. The parameters permit the experimenter to specify a large or small ratio of largest to smallest step size. One can also specify whether these changes should occur suddenly over a short interval or more gradually. The test equation (for which no analytic solution is available) can produce curves which resemble line segments linked by short high-curvature sections. It is related to the harmonic equation, but the sine wave can be distorted into nearly rectangular shape, so that there are alternations of steep and level sections.

This reviewer feels that the paper should be required reading for those who test ODEs. The paper leaves many aspects of testing unaddressed, but the one aspect (step-size adjustment) that it addresses is treated in a competent and effective manner.