Delay Equations, Approximation and Application

1. Front Matter

   Pages 1-12

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2. Approximation Theory and Numerical Methods for Delay Differential Equations

   • Günter Meinardus, Günther Nürnberger

   Pages 13-40

3. Numerical Integration of Retarded Differential Equations with Periodic Solutions

   • H. Arndt, P. J. van der Houwen, B. P. Sommeijer

   Pages 41-51

4. Constrained Mesh Methods for Functional Differential Equations

   • A. Bellen

   Pages 52-70

5. Distribution of Zeros of Polynomial Sequences, Especially Best Approximations

   • H.-P. Blatt, E. B. Saff

   Pages 71-82

6. On a Conjecture about the Critical Points of a Polynomial

   • B. D. Bojanov, Q. I. Rahman, J. Szynal

   Pages 83-93

7. Inclusion of solutions of certain types of linear and nonlinear delay-equations

   • Lothar Collatz

   Pages 94-104

8. Interpolation of Odd Periodic Functions on Uniform Meshes

   • Franz-Jürgen Delvos

   Pages 105-121

9. Simultaneous Interpolation and Norm-Preservation

   • Frank Deutsch

   Pages 122-132

10. Lebesgue Constants and Best Conditions for the Norm Convergensce of Fourier Series

    • B. Dreseler

    Pages 133-146

11. Stochastic Properties of Simple Differential — Delay Equations

    • U. an der Heiden

    Pages 147-164

12. Bivariate Natural Spline Smoothing

    • Chui Li Hu, Larry L. Schumaker

    Pages 165-179

13. Best Approximation by Spline Functions: Theory and Numerical Methods

    • Günther Nürnberger

    Pages 180-212

14. Reconstruction and Approximation of Functions from Samples

    • Q. I. Rahman, G. Schmeisser

    Pages 213-233

15. Time Delay and Doppler Frequency Shift in Radar/Sonar Detection, with Application to Fourier Optics

    • Walter Schempp

    Pages 234-263

16. Uniqueness of Best L1-Approximations of Continuous Functions

    • Manfred Sommer

    Pages 264-281

17. Comparison Theorems in Spline Approximation

    • Hans Strauss

    Pages 282-287

18. The Differential Correction Algorithm

    • G. D. Taylor

    Pages 288-303

19. Ein mathematisches Modell für den Reifungsprozess roter Blutkörperchen bei Neugeborenen

    • H. Werner, C. Fesser

    Pages 304-333

20. On the P-Stability of One-Step Collocation for Delay Differential Equations

    • Marino Zennaro

    Pages 334-343

The international symposium held in October 1984 at the Uni­ versity of Mannheim was the first with the special aim to expose the connection of the Theory of Delay Eauations and Approximation Theory with the emphasis on constructive methods and applications. Although the separate character of both domains is reflected by their historical development, the latest research shows that the numerical treatment of Delay Equations leads to various appro­ ximation and optimization problems. An introductory survey of this circle of problems written by the editors is included at the beginning of the book. Delay Equations have their origin in domains of applications, such as physics, engineering, biology, medicine and economics. They appear in connection with the fundamental problem to analyse a retarded process from the real world, to develop a corresponding mathematical model and to determine the future behavior. Thirty mathematicians attended the conference coming from Germany, West- and Eastern Europe and the United States- more than twenty of them presented a research talk. The lectures about Delay Equations were mainly oriented on the following subjects: single-step, multi-step and spline methods; monotonicity methods for error estimations; asymptotic behavior 10 and periodicity of solutions. The topics of the talks on Approxi­ mation Theory covered different aspects of approximation by poly­ nomials, splines and rational functions and their numerical rea­ lization. Additionally included in the scientific program was a special session on Open Problems, where several suggestions were made for further research concerning both fields.

• Europe
• Germany
• biology
• differential equation
• integration
• medicine
• optimization
• research

• Lehrstuhl für Mathematik IV, Universität Mannheim, Mannheim 1, Germany

  G. Meinardus

• Fakultät für Mathematik und Informatik, Universität Mannheim, Mannheim, Germany

  G. Nürnberger

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