Avoiding order reduction of Runge-Kutta discretizations for linear time-dependent parabolic problems
type: Item
instance of: scholarly article
title: Avoiding order reduction of Runge-Kutta discretizations for linear time-dependent parabolic problems
zbMATH Open document ID: 1050.65084
DOI: 10.1023/B:BITN.0000025087.83146.33
author: I. Alonso-Mallo
author: Begoña Cano
published in: BIT
publication date: 2004-08-06T00:00:00Z
review text: A technique is developed to avoid order reduction when discretizing linear parabolic problems with time dependent operator using Runge-Kutta methods in time and standard schemes in space. The authors improve the time convergence rate for parabolic initial boundary value problems where the operator may depend on time although the boundary operator is still time-independent. It is observed that the derivation of an improved rate in time has only been studied for time- dependent coefficients by \textit{S. L. Keeling} [Math. Comput. 52, No. 186, 561--586 (1989; Zbl 0669.65084)], where an extrapolation technique is used.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 2081526
zbMATH Keywords: order reduction
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: initial boundary value problems
zbMATH Keywords: linear parabolic problems
zbMATH Keywords: convergence
zbMATH Keywords: method of lines
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: b:bitn.0000025087.83146.33
OpenAlex ID: W1974474574
description: scientific article; zbMATH DE number 2081526