Necessary conditions for the stability of difference schemes

V. V. Kucherenko

doi:10.1007/BF01104255

Necessary conditions for the stability of difference schemes

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Abstract

For difference equations of the form uⁿ⁺=Auⁿ+fⁿh, n ≤ T/h the necessary condition for stability due to von Neumann is well known; this condition is expressed in terms of the spectrum of the operator A: r(A)≤1+ch. In this note, for a certain class of difference equations, we express this condition in terms of the spectral radius of the symbol of the operator A.

Original language	English
Pages (from-to)	915-920
Number of pages	6
Journal	Mathematical Notes of the Academy of Sciences of the USSR
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/BF01104255
State	Published - Oct 1974
Externally published	Yes

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title = "Necessary conditions for the stability of difference schemes",

abstract = "For difference equations of the form un+=Aun+fnh, n ≤ T/h the necessary condition for stability due to von Neumann is well known; this condition is expressed in terms of the spectrum of the operator A: r(A)≤1+ch. In this note, for a certain class of difference equations, we express this condition in terms of the spectral radius of the symbol of the operator A.",

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AB - For difference equations of the form un+=Aun+fnh, n ≤ T/h the necessary condition for stability due to von Neumann is well known; this condition is expressed in terms of the spectrum of the operator A: r(A)≤1+ch. In this note, for a certain class of difference equations, we express this condition in terms of the spectral radius of the symbol of the operator A.

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JO - Mathematical Notes of the Academy of Sciences of the USSR

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Necessary conditions for the stability of difference schemes

Abstract

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