Abstract
In this paper we characterize by means of so called root conditions the validity of a class of stability inequalities for linear difference operators. These stability inequalities play a central rôle in proving the convergence of linear multistep methods for initial value problems of first or higher order, where the inhomogeneity satisfies an appropriate Lipschitz condition. Various stability inequalities, concerning the convergence of the solution of the difference equations, are obtained as special cases of our theorems, whereas those used in proving the convergence of higher difference quotients of the solutions of the difference equations are treated with in a subsequent paper. It ist also possible to generalize with analogous methods a so called coerciveness inequality used by GRIGORIEFF [5,6].
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Müller, K.H. (1975). Stabilitätsungleichungen für Lineare Differenzenoperatoren. In: Numerische Behandlung von Differentialgleichungen. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 27. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5532-7_14
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DOI: https://doi.org/10.1007/978-3-0348-5532-7_14
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