Regions of stability, equivalence theorems and the Courant-Friedrichs- Lewy condition
type: Item
instance of: scholarly article
title: Regions of stability, equivalence theorems and the Courant-Friedrichs- Lewy condition
zbMATH Open document ID: 0574.65106
DOI: 10.1007/BF01389633
published in: Numerische Mathematik
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133116
review text: The Courant-Friedrichs-Lewy condition for the discretization of hyperbolic partial differential equations is shown to be equivalent to some results of Jeltsch and Nevanlinna concerning the regions of stability of k-step, m-stage methods for the integration of ordinary differential equations. New equivalence theorems between stability and convergence are provided, which improve on classical results. The paper also characterizes the methods for the numerical integration of the model equation \(u_ t=u_ x\) which are weakly stable when the mesh-ratio takes the maximum value allowed by the CFL condition.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 3917627
zbMATH Keywords: stability regions
zbMATH Keywords: equivalence theorems
zbMATH Keywords: Courant-Friedrichs-Lewy condition
zbMATH Keywords: convergence
author: Jesús María Sanz-Serna
author: Marc N. Spijker
MaRDI profile type: Publication
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OpenAlex ID: W2087261403
description: scientific article; zbMATH DE number 3917627