The Discrete Maximum Principle†

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Abstract
Recently there has been much discussion of the so–called discrete maximum principle. It is now known that this principle is misleading and incorrect in most non–linear examples. In this short note we show that the principle is merely a re–statement of a constrained static variational problem where the constraints represents a cascade of difference equations. In certain linear cases, the overall maximum condition decomposes into cascaded maximum conditions which generate the principle.

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