Slides of this talk (pdf)
This is the first of two talks about stable numeric-geometric methods
for general systems of differential equations with constraints
(so-called differential-algebraic equations or DAE).
Such systems are attracting much attention since they are automatically
generated by computer modeling environments such as MapleSim.
Determination of such constraints is essential for the determination of
consistent initial conditions and the numerical solution of such
This talk will concentrate on introduction of concepts from the (Jet)
geometry of differential equations, illustrated by visualizations and
A subsequent talk by Niloofar Mani, will discuss initial investigations that we have made using MapleSim, and such approaches.
This talk will be an introduction to stable numerical methods for such
The corresponding problem for the non-differential case, that of
approximate polynomial systems, has only recently been given a solution,
through the works of Sommese, Wampler and others. The new area called
numerical algebraic geometry, will also be described.
Key data structures are certain witness points on jet manifolds of
solutions, computed by stable homotopy continuation methods.