Abstract
Integration methods were introduced as a generalization of Runge–Kutta methods in which the index set, usually a set of natural numbers, is replaced by a more complicated alternative, such as a closed interval. Equivalence and reducibility of methods, with an emphasis on the Runge–Kutta case, is considered. Compositions of methods is introduced leading to the composition theorem for integration methods. A number of subgroups of the group of trees are introduced, many of which have a relationship with simplifying assumptions for Runge–Kutta methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Butcher, J.C. (2021). Algebraic Analysis and Integration Methods. In: B-Series. Springer Series in Computational Mathematics, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-030-70956-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-70956-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-70955-6
Online ISBN: 978-3-030-70956-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)