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.
|Number of pages||6|
|Journal||Mathematical Notes of the Academy of Sciences of the USSR|
|State||Published - Oct 1974|