Delay equations, approximation and application

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The international symposium in October 1984 at the University of Mannheim aimed to explore the connection between Delay Equations and Approximation Theory, focusing on constructive methods and applications. Despite their distinct historical developments, recent research indicates that the numerical treatment of Delay Equations leads to various approximation and optimization challenges. An introductory survey by the editors outlines these issues. Delay Equations arise in fields such as physics, engineering, biology, medicine, and economics, addressing the analysis of retarded processes, the development of mathematical models, and the prediction of future behavior. Thirty mathematicians from Germany, West and Eastern Europe, and the United States participated, with over twenty presenting research talks. Lectures on Delay Equations covered topics like single-step, multi-step, and spline methods, error estimation through monotonicity methods, and the asymptotic behavior and periodicity of solutions. Talks on Approximation Theory explored various aspects of approximation using polynomials, splines, and rational functions, along with their numerical realizations. The program also featured a special session on Open Problems, where suggestions for further research in both fields were discussed.