On the starting algorithms for fully implicit Runge-Kutta methods
type: Item
instance of: scholarly article
title: On the starting algorithms for fully implicit Runge-Kutta methods
zbMATH Open document ID: 0970.65081
DOI: 10.1023/A:1022340401909
author: S. González-Pinto
author: S. Pérez-Rodríguez
author: J. I. Montijano
published in: BIT
publication date: 2001-01-25T00:00:00Z
review text: Two types of starting algorithms for solving the algebraic equations arising in the case of fully implicit Runge-Kutta methods for stiff initial value problems are investigated. Their order is related to their efficiency in the case of non-stiff and stiff problems and low required tolerance (global errors). Numerical experiments with four different forms of starting algorithms applied to the Van der Pol and Oregonator models illustrate the theory.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1556489
zbMATH Keywords: solutions of stage equations
zbMATH Keywords: Van der Pol equation
zbMATH Keywords: numerical experiments
zbMATH Keywords: starting algorithms
zbMATH Keywords: fully implicit Runge-Kutta methods
zbMATH Keywords: stiff initial value problems
zbMATH Keywords: Oregonator models
reviewed by: Maria Gousidou-Koutita
MaRDI profile type: Publication
full work available at URL: a:1022340401909
OpenAlex ID: W60958843
description: scientific article; zbMATH DE number 1556489