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On Low Order Embedded Pairs of Implicit Runge-Kutta Formulas

Research output: Book/ReportCommissioned reportProfessional


Original languageEnglish
Place of PublicationTampere
PublisherTampere University of Technology
Number of pages25
ISBN (Electronic)978-952-15-3324-2
ISBN (Print)951-722-559-8
Publication statusPublished - 1996
Publication typeD4 Published development or research report or study

Publication series

NameTampere University of Technology, Dept of Information Technology, Mathematics Report
PublisherTampere University of Technology
ISSN (Print)1236-956X


Implicit Runge-Kutta methods are used for solving stiff ODEs such as those arising in mechanical or electrical system simulation and in semidiscretisation of partial differential equation evolution problems. Embedding one Runge-Kutta formula with another is a way of obtaining an estimate of the local error (for step size control) at a modest computation cost. Our interest is with the design of embedded pairs of low order. We consider both accuracy and basic stability properties of Runge-Kutta formulas with an eye to the performance of the pair as a whole. We present some negative results showing that embedded pairs with certain combinations of stability properties cannot exist. Finally we analyze and compare 7 pairs from the literature and 6 new pairs.

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