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EnglishWe give an overview of the construction of algebraic conditions for determining the order of Runge-Kutta methods and describe a novel extension for numerically solving systems of differential equations. The new schemes, called Elementary Differential Runge-Kutta methods, include as a subset Runge-Kutta methods, Taylor series methods, Multiderivative Runge-Kutta methods. We outline how order conditions have been constructed for the new schemes using B-series and their composition and give details relating to a Mathematica implementation. © 2004 Elsevier B.V.
| Titolo: | On the construction of a new generalization of Runge-Kutta methods | |
| Autore/i: | Sofroniou M.; Spaletta G. | |
| Autore/i Unibo: | ||
| Anno: | 2003 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/S1571-0661(04)80774-6 | |
| Abstract: | We give an overview of the construction of algebraic conditions for determining the order of Runge-Kutta methods and describe a novel extension for numerically solving systems of differential equations. The new schemes, called Elementary Differential Runge-Kutta methods, include as a subset Runge-Kutta methods, Taylor series methods, Multiderivative Runge-Kutta methods. We outline how order conditions have been constructed for the new schemes using B-series and their composition and give details relating to a Mathematica implementation. © 2004 Elsevier B.V. | |
| Data stato definitivo: | 2022-03-31T13:06:32Z | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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