Convergence rates of \(\alpha\)-stable difference methods
type: Item
instance of: scholarly article
title: Convergence rates of \(\alpha\)-stable difference methods
zbMATH Open document ID: 0538.65033
DOI: 10.1016/0021-9045(84)90103-5
author: D. Pontzen
author: E. Goerlich
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: A quantitative Lax type theorem is established with the stability and well-posedness conditions replaced by the weaker concepts of alpha stability and alpha well-posedness. Here ''quantitative'' means that in the consistency hypothesis upon the difference method a rate of convergence is prescribed and that in the convergence result a rate is obtained corresponding to the degree of smoothness of the initial value. This is formulated in a general Banach space first and then made more precise by specializing it to Lebesgue- and Besov spaces. The motivation for the concepts of alpha stability and alpha well-posedness comes from their usefulness in characterizing systems of partial differential equations with constant coefficients and the corresponding difference equations. See the authors [Alpha well-posedness, alpha stability, and the matrix theorems of \textit{H.O. Kreiss}, Numer. Math. (to appear)].
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 65M30
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 3856305
zbMATH Keywords: Banach space
zbMATH Keywords: well-posedness
zbMATH Keywords: semigroup of growth order alpha
zbMATH Keywords: rate of convergence
zbMATH Keywords: Sobolev and Besov spaces
zbMATH Keywords: alpha stability
zbMATH Keywords: consistency
zbMATH Keywords: difference method
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90103-5
OpenAlex ID: W1967418510
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description: scientific article; zbMATH DE number 3856305