Parallel two-step ROW-methods for stiff delay differential equations

In this paper, parallel two-step ROW-methods (PTSROW methods) for the numerical solution to stiff delay differential equations are discussed. The stability behaviors of PTSROW methods are analyzed. It is shown that a PTSROW method is GP-stable or GPL-stable if and only if it is A-stable or L-stable respectively. Furthermore, the order (order of consistency and stage-order) conditions of PTSROW methods by using tree theory and B-series are presented. Some L-stable PTSROW methods and real-time PTSROW methods are constructed. The efficiency of these ROW-methods is shown by some numerical simulation experiments in parallel environment.