The problem of the stability of difference approximations for initial boundary-value problems is examined and recent results obtained in this field by Gustafsson, Kreiss & Sundström (1971) are presented. It is shown that even for scalar equations the Ryabenkii-Godunow condition is not sufficient for stability and a procedure is outlined which leads to a slightly strengthened form of this condition which is satisfactory in practice.
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Heinz‐Otto Kreiss (1971) studied this question.
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