A note on the relative efficiency of Adams methods

AbstractIn several pieces of the most effective mathematical software for non-stiff and mildly stiff initial value problems in ordinary differential equations, the classical Adams methods are implemented in a particular mode. One reason for the choice of mode is sometimes explained in terms of the associated scaled absolute stability regions for the methods. In this note it is shown that the same choice of mode remains appropriate from this point of view when certain families of generalized Adams-type methods are considered