Southern Ontario Numerical Analysis Day

s of Invited Talks C o m p u t e r Algebra for Differential-Algebraic Equat ions (DAEs) Gilles ViUard LMC-IMA G / Equipe Caleul Formel Grenoble, l, ranee This talk will survey the activities of a five year project (95-99) of the computer algebra team of Grenoble on DAEs. The ACTE project has been supported by "Electricit~ de France" (EDF) in relation with the development of the Eurostag software for power systems simulation. Answering to questions of the company EDF, ACTE's main concerns have been to investigate how computer algebra could be involved for the study and the numerical integration of DAEs. Three main topics have been distinguished and will be presented: • The validation of numerical solutions of low index DAEs using global error estimators. Convergence analysis and numerical tests are proposed. • A fully symbolic index reduction algorithm is designed as an effective implementation of Rabier and Rheinbold's method for quasi-linear DAEs. • A cheap hybrid numeric/symbolic is proposed for the numerical integration of high index quasi-linear DAEs. It is based on fast exact linear algebra for a preliminary reduction of the index. Differential-Algebraic Systems in Industr ia l P lant Simulat ion: S o m e Personal Experiences Grant Stephenson Honeywell Hi-Spec Solutions London, Canada In the field of industrial plant simulation, mathematical models of industrial processes are solved to predict plant operation under varying conditions. These models c~a be used for many purposes including plant design, analysis of operating problems, assessment of control strategies, optimization of plant operation and training of plant operators. A plant simulation is typically comprised of a large number of mathematical models each representing some aspect of the processing performed by individual pieces of equipment or the control strategies implemented in the distributed control system. These mathematical models are logically connected to form an integrated model of the plant just as the process piping, electrical wiring and pneumatic tubing connect the equipment in the physical plant. Each equipment model is either a system of nonlinear algebraic equations or differential-algebraic equations. This presentation describes some of the presenter's experiences building and solving mathematical models for piping networks, cryogenic heat exchangers used in natural gas liquefaction and distillation columns in the context of training operators of industrial plants. Solving D D E s in Mat lab Lawrence F. Sharnpine Southern Methodist University, T e x a s With the goal of making it as easy as possible to solve a large class of delay differential equations (DDEs), the speaker and S. Thompson of l:tadford University developed a program, dde23, to solve DDEs with constant delays in Matlab. The speaker will discuss briefly important differences between DDEs and ODEs and then how numerical methods for ODEs can be extended to solve DDEs. Some examples will show that restricting the class of problems, algorithmic developments, language facilities in Mat lab , and design have resulted in a DDE solver that is both very capable and exceptionally easy to use. The solver, a tutorial that shows how to use it by means of many examples from the literature, and complete solutions of the examples are available at http://~mw, tuner, eda/'thompBon/webddes/.