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Numerical Methods for Ordinary Differential Systems The Initial
Value Problem J. D. Lambert Professor of Numerical Analysis
University of Dundee Scotland In 1973 the author published a book
entitled Computational Methods in Ordinary Differential Equations.
Since then, there have been many new developments in this subject
and the emphasis has changed substantially. This book reflects
these changes; it is intended not as a revision of the earlier work
but as a complete replacement for it. Although some basic material
appears in both books, the treatment given here is generally
different and there is very little overlap. In 1973 there were many
methods competing for attention but more recently there has been
increasing emphasis on just a few classes of methods for which
sophisticated implementations now exist. This book places much more
emphasis on such implementations----and on the important topic of
stiffness----than did its predecessor. Also included are accounts
of the structure of variable--step, variable--order methods, the
Butcher and the Albrecht theories for Runge----Kutta methods, order
stars and nonlinear stability theory. The author has taken a middle
road between analytical rigour and a purely computational approach,
key results being stated as theorems but proofs being provided only
where they aid the readera s understanding of the result. Numerous
exercises, from the straightforward to the demanding, are included
in the text. This book will appeal to advanced students and
teachers of numerical analysis and to users of numerical methods
who wish to understand how algorithms for ordinary differential
systems work and, on occasion, fail to work.
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