Comparative analysis of automatic step selection algorithms for stiff Cauchy problems

Automatic step selection algorithms are widely used to solve stiff Cauchy problems. The Gear and Dormand–Prince packages are the most popular ones. These methods are well established being used in soft problems but they can malfunction in stiff ones. Moreover, they do not provide guaranteed error estimation. The cases are known where the real error exceeds the user defined one by many orders of magnitude. In that work the new problem examples are found in which standard algorithms lose robustness.