Stiff Differential Systems

1. Front Matter

   Pages i-x

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2. International Symposium on Stiff Differential Systems

   • Ralph A. Willoughby

   Pages 1-19

3. Composite Multistep Methods and Stiff Stability

   • Theodore A. Bickart, William B. Rubin

   Pages 21-36

4. Numerical A-Stability for Difference-Differential Systems

   • R. K. Brayton

   Pages 37-48

5. Compuation of Real-Time-Control in Aerospace Applications by Multiple Shooting Procedures

   • R. Bulirsch, H.-W. Branca

   Pages 49-50

6. Simulation of Chemical Kinetics Transport in the Stratosphere

   • J. S. Chang, A. C. Hindmarsh, N. K. Madsen

   Pages 51-65

7. The Sets of Smooth Solutions of Differential and Difference Equations

   • Germund Dahlquist

   Pages 67-80

8. Integration Package for Chemical Kinetics

   • Lennart Edsberg

   Pages 81-94

9. Optimal Second Derivative Methods for Stiff Systems

   • W. H. Enright

   Pages 95-109

10. The Stability of Automatic Programs for Numerical Problems

    • C. W. Gear, K. W. Tu, D. S. Watanabe

    Pages 111-121

11. An Implementation of Gear’s Algorithm for CSMP III

    • A. R. Gourlay, H. D. D. Watson

    Pages 123-133

12. A Pseudo Dynamic Method for Solving Nonlinear Algebraic Equations

    • G. Hachtel, M. Mack

    Pages 135-150

13. The Validation and Comparison of Programs for Stiff Systems

    • T. E. Hull

    Pages 151-164

14. Numerical Solution of Singular Perturbation Problems

    • Heinz-Otto Kreiss

    Pages 165-170

15. Two Unconventional Classes of Methods for Stiff Systems

    • J. D. Lambert

    Pages 171-186

16. The Occurrence and Numerical Solution of Physical and Chemical Systems Having Widely Varying Time Constants

    • L. Lapidus, R. C. Aiken, Y. A. Liu

    Pages 187-200

17. A Stiff System Package Based on the Implicit Midpoint Method with Smoothing and Extrapolation

    • Bengt Lindberg

    Pages 201-215

18. Construction of a Family of Second Order, A-Stable K-Step Formulas Depending on the Maximum Number, 2K-2, of Parameters

    • Werner Liniger, Thierry Gagnebin

    Pages 217-227

19. Stiffness and Accuracy in the Method of Lines Integration of Partial Differential Equations

    • A. M. Loeb, W. E. Schiesser

    Pages 229-243

20. Economical Global Error Estimation

    • Hans J. Stetter

    Pages 245-258

The papers in these proceedings were presented at an Inter­ national Symposium on Stiff Differential Systems, which was held at the Hotel Quellenhof, Wildbad, Federal Republic of Germany, October 4-6, 1973. The sumposium was organized by IBM Germany and sponsored by the IBM World Trade Corporation. On behalf of all the participants we wish to express our appreciation to the sponsors and organizers for their generous support,particularly to Dr. G. HUbner, representing Scientific Relations, IBM Germany, and Dr. G. Kozak, representing IBM World Trade Headquarters, New York. The purpose of the conference was to provide an intensive treatment of all apsects of a difficult problem class, stiff differential systems. Some major fields of interest of attendees and contributors are: 1) Modeling and problem solving in scien­ tific and technological applications, 2) Qualitative theory of stiff systems, 3) Numerical Analysis, including design, valida­ tion, and comparison of algorithms, as well as error and stability analysis, and 4) Computer Science, in particular problem-oriented programming languages, program packages, and applications-oriented computer architecture.

• algorithms
• computation
• computer science
• constant
• derivative
• modeling
• numerical analysis
• programming
• programming language

• Mathematical Sciences Department, IBM T. J. Watson Research Center, Yorktown Heights, USA

  Ralph A. Willoughby

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