Skip to main content

Some implementation schemes for implicit Runge-Kutta methods

Part of the Lecture Notes in Mathematics book series (LNM,volume 773)

Keywords

  • Amplification Factor
  • Iteration Scheme
  • Triangular Factor
  • Crude Method
  • Lower Triangular Form

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alexander, R. "Diagonally implicit Runge-Kutta methods for stiff o.d.e.’s", SIAM J. Numer. Anal., 14, 1006–1021 (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bickart, T.A. "An efficient solution process for implicit Runge-Kutta methods", SIAM J. Numer. Anal., 14, 1022–1027 (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Burrage, K. "A special family of Runge-Kutta methods for solving stiff differential equations", BIT, 18, 22–41 (1978).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Burrage, K., Butcher, J.C., and Chipman, F.H. "An implementation of singly-implicit Runge-Kutta methods", Comp. Maths. Report, Univ. of Auckland (in preparation).

    Google Scholar 

  5. Butcher, J.C. "On the implementation of implicit Runge-Kutta methods", BIT, 16, 237–240 (1976).

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Butcher, J.C. "A transformed implicit Runge-Kutta method", Comp. Maths. Report No. 13, Univ. of Auckland (1977).

    Google Scholar 

  7. Butcher, J.C., Burrage, K., and Chipman, F.H. "STRIDE: stable Runge-Kutta integrator for differential equations", Comp. Maths. Report, Univ. of Auckland (in preparation).

    Google Scholar 

  8. Chipman, F.H. "The implementation of Runge-Kutta implicit processes", BIT, 13, 391–393 (1973).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Frank, R., and Überhuber, C.W. "Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations", BIT, 17, 146–159 (1977).

    CrossRef  MathSciNet  Google Scholar 

  10. Frank, R., and Überhuber, C.W. "Collocation and iterated defect correction", Lecture notes in Mathematics 631, 19–34, Springer-Verlag (1978).

    Google Scholar 

  11. Nørsett, S.P. "Semi-explicit Runge-Kutta methods", Math. and Comp. Report No. 6/74, Univ. of Trondheim (1974).

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Butcher, J.C. (1980). Some implementation schemes for implicit Runge-Kutta methods. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094160

Download citation

  • DOI: https://doi.org/10.1007/BFb0094160

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09740-2

  • Online ISBN: 978-3-540-38562-2

  • eBook Packages: Springer Book Archive