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Original scientific paper
https://doi.org/10.2498/cit.2000.01.02

High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers

Jorg Wensch
Rudiger Weiner
Helmut Podhaisky

Fulltext: english, pdf (199 KB) pages 13-18 downloads: 516* cite
APA 6th Edition
Wensch, J., Weiner, R. & Podhaisky, H. (2000). High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers. Journal of computing and information technology, 8 (1), 13-18. https://doi.org/10.2498/cit.2000.01.02
MLA 8th Edition
Wensch, Jorg, et al. "High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers." Journal of computing and information technology, vol. 8, no. 1, 2000, pp. 13-18. https://doi.org/10.2498/cit.2000.01.02. Accessed 11 Apr. 2021.
Chicago 17th Edition
Wensch, Jorg, Rudiger Weiner and Helmut Podhaisky. "High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers." Journal of computing and information technology 8, no. 1 (2000): 13-18. https://doi.org/10.2498/cit.2000.01.02
Harvard
Wensch, J., Weiner, R., and Podhaisky, H. (2000). 'High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers', Journal of computing and information technology, 8(1), pp. 13-18. https://doi.org/10.2498/cit.2000.01.02
Vancouver
Wensch J, Weiner R, Podhaisky H. High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers. Journal of computing and information technology [Internet]. 2000 [cited 2021 April 11];8(1):13-18. https://doi.org/10.2498/cit.2000.01.02
IEEE
J. Wensch, R. Weiner and H. Podhaisky, "High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers", Journal of computing and information technology, vol.8, no. 1, pp. 13-18, 2000. [Online]. https://doi.org/10.2498/cit.2000.01.02

Abstracts
In this paper we study a class of explicit pseudo two-step Runge-Kutta methods (EPTRK methods) with additional weights v. These methods are especially designed for parallel computers. We study s-stage methods with local stage order s and local step order s + 2 and derive a sufficient condition for global convergence order s + 2 for fixed step sizes. Numerical experiments with 4- and 5-stage methods show the influence of this superconvergence condition. However, in general it is not possible to employ the new introduced weights to improve the stability of high order methods. We show, for any given s-stage method with extended weights which fulfills the simplifying conditions B(s) and C(s - 1), the existence of a reduced method with a simple weight vector which has the same linear stability behaviour and the same order.

Hrčak ID: 44848

URI
https://hrcak.srce.hr/44848

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