Speaker
Bertil Gustafsson
Description
Mathematical models for physical processes took a giant
leap when Isaac Newton formulated the basic laws of
mechanics by using differential calculus. In the following
centuries there was a rapid development of mathematical
models for an ever increasing number of scientific and
engineering processes. However, the models are in the form
of differential equations, and in order to make any use of
them for real applications, one has to find the solution in an
explicit analytic form that can be evaluated at any different
point in time and space. Except for very simple problems,
this is impossible. This difficulty is overcome by the use of
numerical methods based on some kind of approximation of
the mathematical model. Such methods were developed for
many problems centuries ago, but their impact were very
limited due to the heavy computations that were required.
The introduction of electronic computers changed the
situation completely. Already known numerical methods
could be implemented and the results could be used for
practical and difficult problems. Furthermore, an almost
explosive development of new numerical methods took
place in parallel with the fast development of computers. In
addition to theory and experiments, science got a third leg:
scientific computing.
In this talk we shall give a survey of the most important
steps of this process, with emphasis on the development of
numerical methods. Furthermore, we shall discuss the
special influence of Swedish researchers, and how it
happened that Sweden got a significant position on the
world map of scientific computing.
