Runge-Kutta time discretizations of parabolic Volterra integro- differential equations
type: Item
instance of: scholarly article
title: Runge-Kutta time discretizations of parabolic Volterra integro- differential equations
zbMATH Open document ID: 0832.65141
published in: Journal of Integral Equations and Applications
publication date: 1996-03-11T00:00:00Z
review text: This article studies optimal convergence of implicit Runge-Kutta methods (of Pouzet type) when applied to abstract Volterra integro-differential equations (including parabolic Volterra integro-partial differential equations). The problem is transformed into a differential equation in an appropriate function space. Since Runge-Kutta methods are invariant under this transformation, optimal convergence results can be obtained from \textit{C. Lubich} and \textit{A. Ostermann} [Runge-Kutta approximation of quasi-linear parabolic equations, Math. Comput. 64, No. 210, 601-627 (1995)]. Numerical examples are included.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 808205
zbMATH Keywords: numerical experiments
zbMATH Keywords: optimal convergence
zbMATH Keywords: implicit Runge-Kutta methods
zbMATH Keywords: abstract Volterra integro-differential equations
zbMATH Keywords: parabolic Volterra integro-partial differential equations
author: H. Brunner
author: J.-P. Kauthen
author: Alexander Ostermann
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075847
OpenAlex ID: W2088142981
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DOI: 10.1216/JIEA/1181075847
description: scientific article; zbMATH DE number 808205