On Low Order Embedded Pairs of Implicit Runge-Kutta Formulas
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Yksityiskohdat
| Alkuperäiskieli | Englanti |
|---|---|
| Julkaisupaikka | Tampere |
| Kustantaja | Tampere University of Technology |
| Sivumäärä | 25 |
| ISBN (elektroninen) | 978-952-15-3324-2 |
| ISBN (painettu) | 951-722-559-8 |
| Tila | Julkaistu - 1996 |
| OKM-julkaisutyyppi | D4 Julkaistu kehittämis- tai tutkimusraportti taikka -selvitys |
Julkaisusarja
| Nimi | Tampere University of Technology, Dept of Information Technology, Mathematics Report |
|---|---|
| Kustantaja | Tampere University of Technology |
| Numero | 71 |
| 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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