Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
A general class of two-step Runge-Kutta methods for ordinary differential equations
SIAM Journal on Numerical Analysis
Order conditions for two-step Runge-Kutta methods
Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Order Conditions for General Two-Step Runge--Kutta Methods
SIAM Journal on Numerical Analysis
Design, analysis and testing of some parallel two-step W-methods for stiff systems
Applied Numerical Mathematics
Parallel Two-Step W-Methods on Singular Perturbation Problems
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
Construction of highly stable two-step W-methods for ordinary differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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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.