Necessary conditions for the stability of difference schemes

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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 languageEnglish
Pages (from-to)915-920
Number of pages6
JournalMathematical Notes of the Academy of Sciences of the USSR
Issue number4
StatePublished - Oct 1974
Externally publishedYes


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