A bound on powers of linear operators, with relevance to numerical stability
نویسندگان
چکیده
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 [l]. @ 2001 Elsevier Science Ltd. All rights reserved. Keywords-Power bounded operators, Resolvent condition, Numerical analysis, Stability analysis, Heat equation, Finite-difference scheme, Crank-Nicholson method.
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ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 15 شماره
صفحات -
تاریخ انتشار 2002