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On Low Order Embedded Pairs of Implicit Runge-Kutta Formulas

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Julkaisun otsikon käännösOn Low Order Embedded Pairs of Implicit Runge-Kutta Formulas
AlkuperäiskieliEnglanti
JulkaisupaikkaTampere
KustantajaTampere University of Technology
Sivumäärä25
ISBN (elektroninen)978-952-15-3324-2
ISBN (painettu)951-722-559-8
TilaJulkaistu - 1996
OKM-julkaisutyyppiD4 Julkaistu kehittämis- tai tutkimusraportti taikka -selvitys

Julkaisusarja

NimiTampere University of Technology, Dept of Information Technology, Mathematics Report
KustantajaTampere University of Technology
Numero71
ISSN (painettu)1236-956X

Tiivistelmä

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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