On the numerical solution of stiff IVPs by Lobatto IIIA Runge-Kutta methods
type: Item
instance of: scholarly article
title: On the numerical solution of stiff IVPs by Lobatto IIIA Runge-Kutta methods
zbMATH Open document ID: 0886.65079
DOI: 10.1016/S0377-0427(97)00086-1
author: J. I. Montijano Torcal
author: S. González-Pinto
author: S. Pérez-Rodríguez
published in: Journal of Computational and Applied Mathematics
publication date: 1998-04-14T00:00:00Z
review text: The authors introduce new iterative schemes (so called single-Newton schemes) to the solution of the implicit equations in the \(s\)-stage Lobatto IIIA methods and study the linear stability properties of these schemes. Especially the effective constructions for the three-stage, fourth-order and for the four-stage, sixth-order Lobatto IIIA are considered. Their stability regions approximate to the negative complex half-plane as the number of iterations increases. Numerical results for the three following problems are presented: the Oregonator, the Van der Pol oscillator and the CUSP problem. The authors compare their code with three well-known codes for the solution of stiff systems: EPISODE, STRIDE and RADAU5. Lobatto IIIA formulae with the new iterative schemes can be competitive with standard codes used in solving stiff systems.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34E13
zbMATH DE Number: 1084094
zbMATH Keywords: stability regions
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: Lobatto IIIA formulae
zbMATH Keywords: iterative schemes
zbMATH Keywords: oregonator
zbMATH Keywords: Van der Pol oscillator
zbMATH Keywords: CUSP problem
zbMATH Keywords: stiff systems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1084094