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Numerical Methods for Conservation Laws (Paperback, Softcover reprint of the original 2nd ed. 1992)
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Numerical Methods for Conservation Laws (Paperback, Softcover reprint of the original 2nd ed. 1992)
Series: Lectures in Mathematics. ETH Zurich
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These notes developed from a course on the numerical solution of
conservation laws first taught at the University of Washington in
the fall of 1988 and then at ETH during the following spring. The
overall emphasis is on studying the mathematical tools that are
essential in de veloping, analyzing, and successfully using
numerical methods for nonlinear systems of conservation laws,
particularly for problems involving shock waves. A reasonable un
derstanding of the mathematical structure of these equations and
their solutions is first required, and Part I of these notes deals
with this theory. Part II deals more directly with numerical
methods, again with the emphasis on general tools that are of broad
use. I have stressed the underlying ideas used in various classes
of methods rather than present ing the most sophisticated methods
in great detail. My aim was to provide a sufficient background that
students could then approach the current research literature with
the necessary tools and understanding. Without the wonders of TeX
and LaTeX, these notes would never have been put together. The
professional-looking results perhaps obscure the fact that these
are indeed lecture notes. Some sections have been reworked several
times by now, but others are still preliminary. I can only hope
that the errors are. not too blatant. Moreover, the breadth and
depth of coverage was limited by the length of these courses, and
some parts are rather sketchy."
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