How to avoid accuracy and order reduction in Runge–Kutta methods as applied to stiff problems
| Autor: | L. M. Skvortsov |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematical optimization
Order reduction Diagonal 010103 numerical & computational mathematics 01 natural sciences Stiff equation Mathematics::Numerical Analysis 010101 applied mathematics L-stability Computational Mathematics Runge–Kutta methods Order (business) Applied mathematics 0101 mathematics Reduction (mathematics) Mathematics |
| Zdroj: | Computational Mathematics and Mathematical Physics. 57:1124-1139 |
| ISSN: | 1555-6662 0965-5425 |
| DOI: | 10.1134/s0965542517070119 |
| Popis: | The solution of stiff problems is frequently accompanied by a phenomenon known as order reduction. The reduction in the actual order can be avoided by applying methods with a fairly high stage order, ideally coinciding with the classical order. However, the stage order sometimes fails to be increased; moreover, this is not possible for explicit and diagonally implicit Runge–Kutta methods. An alternative approach is proposed that yields an effect similar to an increase in the stage order. New implicit and stabilized explicit Runge–Kutta methods are constructed that preserve their order when applied to stiff problems. |
| Databáze: | OpenAIRE |
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