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A general equivalence theorem in the theory of discretization methods

Authors: J. M. Sanz-Serna and C. Palencia
Journal: Math. Comp. 45 (1985), 143-152
MSC: Primary 65J10; Secondary 65M10, 65N10
MathSciNet review: 790648
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Abstract: The Lax-Richtmyer theorem is extended to work in the framework of Stetter's theory of discretizations. The new result applies to both initial and boundary value problems discretized by finite elements, finite differences, etc. Several examples are given, together with a comparison with other available equivalence theorems. The proof relies on a generalized Banach-Steinhaus theorem.

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Article copyright: © Copyright 1985 American Mathematical Society