Equilibrium states for predictor-corrector methods (Q1128077)

Step control (SC) stability is a theory that explains the stepsize patterns of numerical methods with bounded stability regions when they are applied with variable stepsizes to stiff or mildly stiff problems. In the present article, SC-stability is studied for the Adams multistep methods of orders 1 to 4 (in predictor corrector mode). It is shown that most of these methods have difficulties (frequent step rejections) with mildly stiff problems where the dominant eigenvalue of the Jacobian is real. Some numerical experiments illustrate the theoretical results.