Abstract
This paper explores methods of DIMSIM structure, with coefficient matrix of the form A = λ I, allowing the stages to be evaluated in parallel. It is found that many of these methods possess a strong A-stable property making them suitable for the solution of large stiff problems.
Similar content being viewed by others
References
J. C. Butcher, Diagonally-implicit multi-stage integration methods, Appl. Numer. Math. 11 (1993) 347–363.
J. C. Butcher, A transformation for the analysis of DIMSIMs, BIT 34 (1994) 25–32.
P. E. Chartier, L-stable parallel one-block methods for ordinary differential equations, SIAM J. Numer. Anal. (1994).
A. Iserles and S. P. Nørsett, On the theory of parallel Runge-Kutta methods, IMA J. Numer. Anal. 10 (1990) 463–488.
G. Polya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis (Springer, Berlin, 1925).
P. J. van der Houwen and B. P. Sommeijer, Parallel iteration of high-order Runge-Kutta methods with stepsize control, J. Comput. Appl. Math. 29 (1990) 111–127.
E. T. Whitaker and G. N. Watson, A Course of Modern Analysis (Cambridge University Press, 1915).
Rights and permissions
About this article
Cite this article
Butcher, J.C. Order and stability of parallel methods for stiff problems. Advances in Computational Mathematics 7, 79–96 (1997). https://doi.org/10.1023/A:1018934516771
Issue Date:
DOI: https://doi.org/10.1023/A:1018934516771