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.
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. © 2004 Elsevier B.V.File in questo prodotto:
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