Numeric-Geometric Techniques for Differential Equations
II. Applications
Niloofar Mani
University of Western Ontario
There are software packages that support high-level physics-based modeling
and simulation. One of the latest is MapleSim which allows you to build
component diagrams that represent physical systems in a graphical form. Using
both symbolic and numeric approaches, this software automatically generates
model differential equations with constraints (so-called
differential-algebraic equations or DAE) from a component diagram and runs
high-fidelity simulations.
We describe initial steps towards using geometric methods including homotopy
continuation to analyze and help solve such systems numerically. This talk is
a sequel to the introductory talk by Greg Reid, earlier in this session. The
geometric methods have the advantage of numerical stability compared with
symbolic differential-elimination methods, which much like Gauss elimination,
can be unstable due to pivots on small approximate quantities. The talk will
be illustrated by examples and applications.