Numerische Mathematik

, Volume 41, Issue 2, pp 223–253

Die gleichmäßige Stabilität singulär gestörter diskreter und kontinuierlicher Randwertprobleme

  • Klaus Niederdrenk
  • Harry Yserentant
Reductibility of a Linear Differential System

DOI: 10.1007/BF01390214

Cite this article as:
Niederdrenk, K. & Yserentant, H. Numer. Math. (1983) 41: 223. doi:10.1007/BF01390214

The uniform stability of singularly perturbed discrete and continuous boundary value problems

Summary

In this paper we consider singular perturbation problems for ordinary differential operators of ordern and their discrete counterparts on arbitrary nonuniform grids. We prove that the singularly perturbed initial value problem is stable uniformly in the perturbation parameter ε in both the continuous and the discrete case. We use this result to characterize the stability of the corresponding continuous and discrete boundary value problems. If the continuous problem is stable and if the consistency error is smaller than a certain constant, the discrete problem is also stable.

Subject Classifications

AMS: 65L05 65L10 34D15 CR: 5.17 

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Klaus Niederdrenk
    • 1
  • Harry Yserentant
    • 2
  1. 1.Rechenzentrum der RWTH AachenAachen
  2. 2.Institut für Geometrie und Praktische Mathematik der RWTH AachenAachen

Personalised recommendations