8:45 AM / Monday, February 12, 1996

Invited Presentation 1
Automatic Differentiation and Implicit Differential Equations

Many physical processes are most naturally and easily modeled as mixed systems of differential and algebraic equations (DAEs), and there has been an increased interest in exploiting the advantages of working directly with these implicit models. Differentiation plays an important role in both the analysis and numerical solution of DAEs, and automatic differentiation can have a significant impact on what is considered a practical approach and what types of problems can be solved. However, working with DAEs places special demands on automatic differentiation codes. More is required than just computing a gradient reasonably quickly.

The speaker will present a brief introduction to DAEs and the role of differentiation when working with DAEs. He will discuss the requirements that DAEs make on automatic differentiation software, and present some of his own experience in using automatic differentiation software. Automatic differentiation software has a significant role to play in the future for DAEs but not all of the demands that the numerical solution of DAEs places on automatic differentiation software are currently being met. If time permits, the speaker will discuss some related problems in nonlinear control which make similar use of automatic differentiation.

Stephen L. Campbell
North Carolina State University

MEM, 12/28/95