Optimal convergence results for Runge-Kutta discretizations of linear nonautonomous parabolic problems
type: Item
instance of: scholarly article
title: Optimal convergence results for Runge-Kutta discretizations of linear nonautonomous parabolic problems
zbMATH Open document ID: 0921.65068
DOI: 10.1023/A:1022369208270
author: Cesáreo Ganzález
author: Alexander Ostermann
published in: BIT
publication date: 1999-05-25T00:00:00Z
review text: The convergence properties of implicit Runge-Kutta methods for the time-discretization of linear nonautonomous parabolic problems is analyzed. The authors work in an abstract Banach space setting that covers standard parabolic initial-boundary value problems with time-dependent smooth coefficients. The Runge-Kutta methods are only assumed to be \(A (\theta)\)-stable, and variable stepsizes are allowed in the analysis. As the main result optimal convergence rates for Runge-Kutta discretizations of temporally smooth solutions are derived.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 1275243
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: abstract parabolic equations
zbMATH Keywords: time-discretization
zbMATH Keywords: Banach space
zbMATH Keywords: convergence
zbMATH Keywords: variable stepsizes
zbMATH Keywords: error bounds
zbMATH Keywords: parabolic initial-boundary value problems
zbMATH Keywords: time-dependent smooth coefficients
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1275243