Abstract
For difference equations of the form un+=Aun+f nh, 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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Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 545–552, October, 1974.
The author thanks V. P. Maslov for a discussion of the results of this paper and for useful remarks.
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Kucherenko, V.V. Necessary conditions for the stability of difference schemes. Mathematical Notes of the Academy of Sciences of the USSR 16, 915–920 (1974). https://doi.org/10.1007/BF01104255
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DOI: https://doi.org/10.1007/BF01104255