Title:  Improved Structural Analysis for Solving High-Index DAEs

Ned Nedialkov and John Pryce are the authors of DAETS, a C++ code for solving high-index, any order differential-algebraic equations (DAEs). It uses Pryce's structural analysis (SA) theory, and expands the solution in Taylor series using automatic differentiation. DAETS is very effective when high accuracy is required and at solving problems of high index: we have solved artificial DAEs of index up to 47.
The consistent initialization of a DAE, one of the difficult problems in DAE solving, is handled naturally in DAETs by solving a least-squares optimization problem. However, the original SA of Pryce may require more initial values than necessary for computing a solution. We develop a method based on the Dulmage-Mendelsohn decomposition for substantially reducing the number of variables needed for consistent initialization.
This talk will outline the theory and algorithms behind DAETs, present our improved SA, and show examples on which our method reduces drastically the number of initial conditions.
Joint work with John Pryce and Azzam Hazim.