BibTeX
@MISC{Seidman_onthe,
author = {Thomas I. Seidman},
title = {On the Stability of Certain Difference Schemes* By},
year = {}
}
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Abstract
The von Neumann stability criterion is employed in analyzing the stability of a class of difference schemes for initial-value problems involving linear parabolic partial differential equations, u t = A u. It is shown that, contrary to the usual rule of thumb, there exist completely implicit difference schemes which are unconditionally unstable. Further, it is shown that the stability properties of certain sets of corresponding schemes are closely related. (I) We consider the linear parabolic partial differential equation for u=u(m, t) us--Au=O where
