JournalsowrVol. 3 / No. 2DOI 10.4171/owr/2006/18

Differential-Algebraic Equations

  • Stephen L. Campbell

    North Carolina State University, Raleigh, United States
  • Roswitha März

    Humboldt-Universität zu Berlin, Germany
  • Linda Petzold

    University of California, Santa Barbara, United States
  • Peter Rentrop

    TU München, Germany
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Abstract

The topic of Differential Algebraic Equations (DAEs) began to attract significant research interest in applied and numerical mathematics in the early 1980's. Today, a quarter of a century later, DAEs are an independent field of research, which is gaining in importance and becoming of increasing interest for both applications and mathematical theory.\\ This Oberwolfach workshop brought together 48 experts in applied mathematics, among them, on the one hand, some who have already influenced and formed the developments of the field, and on the other hand, some very young researchers who have shown outstanding creativity and competence in connection with their PhD theses and thus raise great hopes for further advances.\\ The 16 female and 32 male scientists came from 13 countries to meet and work together in the wonderful, unique Oberwolfach atmosphere, which stimulated a fruitful and pleasant collaboration.\\ The schedule comprised a total of 34 presentations, 18 of which were arranged into 14 survey lectures (some of them with more than one speaker) offering a broader treatment of a particular subject. 16 shorter contributions supplemented the scientific programmme. The areas can be classified (of course with large overlap) into 4 groups: \begin{itemize} \item abstract differential algebraic systems, coupled systems, partial differential algebraic systems; \item analysis of (ordinary) differential algebraic equations and application of numerical methods to problems having new mathematical complexity; \item innovative and improved numerical integration methods to solve highly complex application problems; \item optimization with constraints described by DAEs and control problems concerning DAEs. \end{itemize} The broad range of these areas and the diversity of the participants stimulated fruitful discussions between the different branches and gave rise to new contacts and collaborations. A considerable gain in knowledgde and progress became obvious, which includes the formulation of open questions and challenges for the future.\\ We are grateful to the Mathematisches Forschungsinstitut Oberwolfach for providing an inspiring setting for this workshop.