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. © 2003 Published by Elsevier Science B. V.
Sofroniou, M., Spaletta, G. (2003). On the construction of a new generalization of Runge-Kutta methods. ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE, 74, 189-206 [10.1016/S1571-0661(04)80774-6].
On the construction of a new generalization of Runge-Kutta methods
Spaletta G.
2003
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. © 2003 Published by Elsevier Science B. V.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
