On the lack of convergence of unconditionally stable explicit rational Runge-Kutta schemes
type: Item
instance of: scholarly article
title: On the lack of convergence of unconditionally stable explicit rational Runge-Kutta schemes
zbMATH Open document ID: 0611.65057
DOI: 10.1016/0045-7825(86)90011-3
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1986-01-01T00:00:00Z
review text: The authors investigate convergence properties of rational Runge-Kutta methods, when they are applied to ordinary differential equations which arise from the spatial discretization of \(u_ t-Cu_ x=0\) (hyperbolic equation) and \(u_{tt}-Du_{xx}=0\) (parabolic equation). Although the considered methods are consistent and unconditionally stable, it is shown that they are not convergent if the time steps are too large. This demonstrates the limited applicability of such time-integration schemes.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 3988645
zbMATH Keywords: consistency
zbMATH Keywords: unconditional stability
zbMATH Keywords: rational Runge-Kutta methods
zbMATH Keywords: time- integration schemes
author: Anthony Peirce
author: Jean H. Prévost
MaRDI profile type: Publication
full work available at URL: 0045-7825(86)90011-3
OpenAlex ID: W1993847096
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description: scientific article; zbMATH DE number 3988645