Preserving algebraic invariants with Runge-Kutta methods
type: Item
instance of: scholarly article
title: Preserving algebraic invariants with Runge-Kutta methods
zbMATH Open document ID: 0969.65069
DOI: 10.1016/S0377-0427(00)00459-3
author: Antonella Zanna
author: Arieh Iserles
published in: Journal of Computational and Applied Mathematics
publication date: 2001-09-25T00:00:00Z
review text: The authors introduce a generalized class of Runge-Kutta schemes, namely Lie-group-type Runge-Kutta methods, designed to solve ordinary differential equations on Lie groups, and to preserve a large class of algebraic invariants. The conditions for the retention of algebraic invariants are imposed on the coefficients of the methods and a pair of partial differential equations that must be obeyed by the invariants. It is also proved that Runge-Kutta schemes cannot preserve any polynomial conservation law except for linear and quadratic.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 1566003
zbMATH Keywords: initial value problems
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: algebraic invariants
zbMATH Keywords: Lie groups
reviewed by: Dana Petcu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1566003