COMPUTATIONAL MATHEMATICS
Fundamental physical phenomena have mathematical descriptions
in terms of equations. The objective of computational mathematics
is to study certain mathematical aspects of these equations and
their solutions. The results are intended to deepen the mathematical
knowledge of such equations and thereby carry across to physical
understanding of phenomena that the equations describe. In addition
to applications in the physical sciences, such as in material
sciences, computational mathematics has been applied to finance,
biology, and system analysis.
Waves, light, gravity, and elementary particle interactions are
described mathematically in terms of wave equations and physical
field equations. The purpose of ANCO's,
CRAIG's, and WOLF's
research is to study these kinds of equations, focusing in particular
on symmetries, conservation laws, and properties of their solutions.
Spatially descrete dynamical
systems are often used to model phenomena involving locally interacting
objects, such as, for example, granular flow and road traffic
flow. FUKS is interested in kinetic phase
transitions occuring in such models, development of singularities
in their flow diagrams, and their possible connections with article-based
models of parallel computation.