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Conference on the Numerical Solution of Differential Equations pp 55–63Cite as

The development of software for solving ordinary differential equations

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 363))

Abstract

Factors involved in the development of good software are discussed, with particular reference to programs for solving ODE's. These factors include the basic structuring of the programs themselves, along with the appropriateness of various language facilities, comparisons of efficiency, proofs of correctness, certification and distribution, etc.

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Bibliography

  1. James M. Boyle, William J. Cody, Wayne R. Cowell, Burton S. Garbow, Yasuhiko Ikebe, Cleve B. Moler, Brian T. Smith, "NATS, A Collaborative Effort to Certify and Disseminate Mathematical Software", Proceedings, ACM Conference (1972), pp. 630–635.

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  2. W.H. Enright, "Studies in the Numerical Solution of Stiff Ordinary Differential Equations", Ph.D. thesis, Department of Computer Science, University of Toronto (1972).

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  3. B. Ford, "The Nottingham Algorithms Group (NAG) Project", SIGNUM Newsletter, 8 2 (April, 1973), pp. 16–21.

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  4. G. Hall, W.H. Enright, T.E. Hull, A.E. Sedgwick, "DETEST: A Program for Comparing Numerical Methods for Ordinary Differential Equations", Technical Report, Department of Computer Science, University of Toronto, in preparation.

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  5. T.E. Hull, "The Numerical Integration of Ordinary Differential Equations", IFIP Congress 68, Proceedings, (North-Holland, Amsterdam, 1968), pp. 131–144.

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  6. T.E. Hull, "The Effectiveness of Numerical Methods for Ordinary Differential Equations", SIAM Studies in Num Anal 2 (1970), pp. 114–121.

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  7. T.E. Hull, W.H. Enright, B.M. Fellen, A.E. Sedgwick, "Comparing Numerical Methods for Ordinary Differential Equations", SIAM J Num Anal, 9, 4 (December, 1972), pp. 603–637.

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  8. T.E. Hull, W.H. Enright, A.E. Sedgwick, "The Correctness of Numerical Algorithms", Proceedings of the SIGPLAN Symposium on Proofs of Assertions about Programs, Las Cruces, New Mexico (1972), pp. 66–73.

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  9. T.E. Hull, W.H. Enright, A.E. Sedgwick, "The Structure of Programs for Ordinary Differential Equations", Technical Report, Department of Computer Science, University of Toronto, in preparation.

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  10. T.E. Hull and J.J. Hofbauer, "Language Facilities for Numerical Computation", Technical Report, Department of Computer Science, University of Toronto, in preparation.

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  11. Arthur Sedgwick, "An Effective Variable Order Variable Step Adams Method", Ph.D. thesis, Department of Computer Science, University of Toronto (1973).

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  12. A.E. Sedgwick and C.A. Steele, "DEFT: A Disciplined Extension of FORTRAN", Technical Report, Department of Computer Science, University of Toronto, in preparation.

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Authors
  1. T. E. Hull
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G. A. Watson

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© 1974 Springer-Verlag

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Hull, T.E. (1974). The development of software for solving ordinary differential equations. In: Watson, G.A. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069125

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  • DOI: https://doi.org/10.1007/BFb0069125

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06617-0

  • Online ISBN: 978-3-540-37914-0

  • eBook Packages: Springer Book Archive

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