A bound on powers of linear operators, with relevance to numerical stability Original Research Article

In this note, we formulate a theorem giving bounds on the powers of linear operators, in a general Banach space setting. The relevance of the theorem is illustrated by applying it to the Crank-Nicholson method for the numerical solution of the heat equation. This application yields a stability estimate in the maximum norm which amounts to an improvement over a well-known result of Serdjukova [1].