Abstract
In this follow-up to a paper on the stability of one-step schemes for first-order problems, the stability of more general finite difference schemes is related explicitly to the stability of the continuous mth order system being solved. At times, this gives materially better estimates for the stability constant than those obtained by the standard process of appealing to the stability of the numerical scheme for the associated initial value problem. The argument uses a novel smooth approximant f to given data (on an arbitrary mesh) for which ${{\|D^m f\|_\infty } / {m!}}$ is bounded by the absolutely largest mth divided difference of the data.
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