Skip to main content
SpringerLink
Log in

Difficulties in evaluating differential equation software

  • Conference paper
  • First Online:
Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 909))

  • 464 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Crowder, R.S. Dembo, and J.M. Mulvey, On reporting computational experiments with mathematical software, ACM trans. on Math. Software 5 (1979), 193–203.

    Article  Google Scholar 

  2. R.D. Russell and J.M. Varah, A comparison of global methods for linear two-point boundary value problems, Math. of Comp. 29 (1975), 1–13.

    Article  MathSciNet  MATH  Google Scholar 

  3. R.D. Russell, Efficiencies of B-spline methods for solving differential equations, Proc. 5th Manitoba Conference on Numerical Mathematics, Utilitas Math. (1975), 599–617.

    Google Scholar 

  4. J.C. Diaz, G. Fairweather, and P. Keast, A comparative study of finite element methods for the solution of second order linear two-point boundary value problems, Dept. of Computer Science Tech. Report 150/81, Univ. Toronto (1981).

    Google Scholar 

  5. H.B. Keller, Numerical solution of boundary value problems for ordinary differential equations: survey and some recent results on difference methods, Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations, A.K. Aziz, ed., Academic Press, New York, 1975.

    Google Scholar 

  6. R.D. Russell, A comparison of collocation and finite differences for solving two-point boundary value problems, SIAM J. Numer. Anal. 14 (1977), 19–39.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Bulirsch, J. Stoer, and P. Deuflhard, Numerical solution of nonlinear two-point boundary value problems I, Numer. Math. Handbook Series Approximation (1976).

    Google Scholar 

  8. M.L. Scott and H.A. Watts, Computational solutions of linear two-point boundary value problems via orthonormalization, SIAM J. Numer. Anal. 14 (1977), 40–70.

    Article  MathSciNet  MATH  Google Scholar 

  9. I. Gladwell, Shooting codes in the NAG library, Codes for Boundary-Value Problems in Ordinary Differential Equations, B. Childs et al., ed., Springer-Verlag Lecture Notes in Computer Science 26 (1979).

    Google Scholar 

  10. M. Lentini and V. Pereyra, An adaptive finite difference solver for nonlinear two-point boundary value problems with mild boundary layers, SIAM J. Numer. Anal. 14 (1977), 91–111.

    Article  MathSciNet  MATH  Google Scholar 

  11. U. Ascher, J. Christiansen, and R.D. Russell, Collocation software for boundary value ODE's, ACM Trans. on Math. Software (1981).

    Google Scholar 

  12. J. Christiansen and R.D. Russell, Deferred corrections using uncentered end formulas, Num. Math. 35 (1980), 21–33.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Kahaner, Comparison of numerical quadrature formulas, in Mathematical Software, ed. by J. Rice, Academic Press, New York (1971), 229–259.

    Google Scholar 

  14. L.F. Shampine, H.A. Watts, and S.M. Davenport, Solving nonstiff ordinary differential equations—the state of the art, SIAM Review 18 (1976), 376–411.

    Article  MathSciNet  MATH  Google Scholar 

  15. V. Pereyra and R.D. Russell, Difficulties of comparing complex mathematical software: general comments and the BVODE case, manuscript (1981).

    Google Scholar 

  16. V. Pereyra, Solución numérica de ecuaciones diferenciales con valores de frontera, Acta Cient. Venezolana 30 (1979), 7–22.

    MathSciNet  Google Scholar 

  17. U. Ascher and R.D. Russell, Reformulation of boundary value problems into “standard” form, SIAM Review 23 (1981), 238–254.

    Article  MathSciNet  MATH  Google Scholar 

  18. P.W. Hemker, h. Schippers, and P.M. de Zeeuw, Comparing some aspects of two codes for two-point boundary-value problems, Math. Centrum Report NW 98/80, Amsterdam (1980).

    Google Scholar 

  19. K.L. Hiebert, A comparison of software which solves systems of nonlinear equations, Sandia Labs Report SAND 79-0483, Albuquerque, N.M. (1979).

    Google Scholar 

  20. K.L. Hiebert, A comparison of nonlinear least squares software, Sandia Labs Report 80-0181, Albuquerque, N.M. (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    Robert D. Russell

Authors
  1. Robert D. Russell
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. P. Hennart

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Russell, R.D. (1982). Difficulties in evaluating differential equation software. In: Hennart, J.P. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092972

Download citation

  • DOI: https://doi.org/10.1007/BFb0092972

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11193-1

  • Online ISBN: 978-3-540-38986-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation