Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Embedded diagonally implicit Runge-Kutta algorithms on parallel computers


Authors: P. J. van der Houwen, B. P. Sommeijer and W. Couzy
Journal: Math. Comp. 58 (1992), 135-159
MSC: Primary 65L06; Secondary 65Y05
MathSciNet review: 1106986
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper investigates diagonally implicit Runge-Kutta methods in which the implicit relations can be solved in parallel and are singly diagonal-implicit on each processor. The algorithms are based on diagonally implicit iteration of fully implicit Runge-Kutta methods of high order. The iteration scheme is chosen in such a way that the resulting algorithm is $ A(\alpha )$-stable or $ L(\alpha )$-stable with $ \alpha $ equal or very close to $ \pi /2$. In this way, highly stable, singly diagonal-implicit Runge-Kutta methods of orders up to 10 can be constructed. Because of the iterative nature of the methods, embedded formulas of lower orders are automatically available, allowing a strategy for step and order variation.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L06, 65Y05

Retrieve articles in all journals with MSC: 65L06, 65Y05


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1106986-8
PII: S 0025-5718(1992)1106986-8
Keywords: Runge-Kutta methods, parallelism
Article copyright: © Copyright 1992 American Mathematical Society