Contemporary Mathematics
Volume 99, 1989
R. Temaml
The considerable increase in the computing power which is now
available, brings us to the point where we can contemplate the resolution
of very complicated problems which were unthinkable a few years ago; this
trend may even improve within a few years if the present evolution in the
technology of computers continues.
Following the important literature which appeared recently concerning
the numerical study and the simulation of finite dimensional dynamical
systems the subsequent natural step is to consider more complicated systems
producing more complicated phenomena, including pattern formations in space
(or in the space like variables) when many variables or degrees of freedom
are involved. At the same time the engineers and scientists doing large
scale computations are reaching the point where, after discretization, the
partial differential equations of mathematical physics (or, as well, of
mechanics, chemistry, ... ) produce finite dimensional dynamical systems
involving non trivial phenomena: i.e. for the values of the parameters
which are of physical interest and within the range of the present
computers, nontrivial dynamical phenomena may occur such as bifurcations,
or even the occurence of more chaotic and more complex flows. This
lLaboratoire d'Analyse Numerique, Universite Paris Sud,
Orsay, France
1989 American Mathematical Society
0271-4132/89 $1.00
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