On Low Order Embedded Pairs of Implicit Runge-Kutta Formulas
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Details
| Original language | English |
|---|---|
| Place of Publication | Tampere |
| Publisher | Tampere University of Technology |
| Number of pages | 25 |
| ISBN (Electronic) | 978-952-15-3324-2 |
| ISBN (Print) | 951-722-559-8 |
| Publication status | Published - 1996 |
| Publication type | D4 Published development or research report or study |
Publication series
| Name | Tampere University of Technology, Dept of Information Technology, Mathematics Report |
|---|---|
| Publisher | Tampere University of Technology |
| No. | 71 |
| ISSN (Print) | 1236-956X |
Abstract
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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