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CONVERGENCE AND STABILITY FOR A HYPERBOLIC DIFFERENCE EQUATION WITH ANALYTIC INITIAL-VALUES

GERMUND DAHLQUIST
Mathematica Scandinavica
Vol. 2, No. 1 (August 4, 1954), pp. 91-102
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24488981
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
CONVERGENCE AND STABILITY FOR A HYPERBOLIC DIFFERENCE EQUATION WITH ANALYTIC INITIAL-VALUES
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Abstract

The passage to the limit from a simple hyperbolic difference equation to a partial differential equation is investigated. It is shown that the solution of the difference equation tends to that of the differential equation (even if a certain criterion of Courant, Friedrichs and Lewy is not satisfied), when the initial values satisfy certain conditions of analyticity. In numerical computations, however, the round-off errors usually destroy the delicate features which make the formal convergence possible.

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