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Zur Stabilität von Differenzenverfahren für Systeme linearer gewöhnlicher Randwertaufgaben

On the stability of difference approximations to systems of linear ordinary boundary value problems

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Summary

In this paper we give a simple stability theory for finite difference approximations to linear ordinary boundary value problems. In particular we consider stability with respect to a maximum norm including all difference quotients up to the order of the differential equation. It is shown that stability in this sense holds if and only if the principal part of the differential equation is discretized in a “stable way”. This last property is characterized by root conditions which we prove to be satisfied for some classes of finite difference schemes. Our approach simplifies and generalizes some known results of the literature where Sobolev norms or merely the maximum norm are used.

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  1. Institut für Numerische und Instrumentelle Mathematik der Universität Münster, Roxeler Str. 64, D-4400, Münster, Germany (Fed. Rep.)

    Wolf-Jürgen Beyn

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Beyn, WJ. Zur Stabilität von Differenzenverfahren für Systeme linearer gewöhnlicher Randwertaufgaben. Numer. Math. 29, 209–226 (1978). https://doi.org/10.1007/BF01390339

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