On the iterative solution of the algebraic equations in fully implicit Runge--Kutta methods
type: Item
instance of: scholarly article
title: On the iterative solution of the algebraic equations in fully implicit Runge--Kutta methods
zbMATH Open document ID: 0947.65084
DOI: 10.1023/A:1019195816194
author: S. González-Pinto
author: Manuel Calvo
author: J. I. Montijano
published in: Numerical Algorithms
publication date: 2000-06-07T00:00:00Z
review text: The paper is concerned with the iterative solution of stage equations given by a fully implicit Runge-Kutta method applied to stiff ordinary differential equations. The single-Newton iterative schemes defined here require only one LU-factorization per step and so the methods are preferable to other iterative schemes. The behavior of the iteration errors, independent of the stiffness, for single-Newton schemes and also for Newton-type iterations in general Runge-Kutta methods, is discussed. Finally, the results of some numerical experiments which confirm the theory are presented.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1456936
zbMATH Keywords: initial value problems
zbMATH Keywords: stiff systems
zbMATH Keywords: implicit Runge-Kutta methods
zbMATH Keywords: solvability of stage equations
zbMATH Keywords: convergence
zbMATH Keywords: single-Newton iterative schemes
zbMATH Keywords: numerical experiments
reviewed by: Iulian Coroian
MaRDI profile type: Publication
full work available at URL: a:1019195816194
OpenAlex ID: W1655797795
description: scientific article; zbMATH DE number 1456936