Skip to main content
SpringerLink
Log in

Some implementation schemes for implicit Runge-Kutta methods

  • Conference paper
  • First Online:
Book cover Numerical Analysis

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

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 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
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. Alexander, R. "Diagonally implicit Runge-Kutta methods for stiff o.d.e.’s", SIAM J. Numer. Anal., 14, 1006–1021 (1977).

    Article  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).

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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).

    Article  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).

    Article  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).

    Article  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
  1. J. C. Butcher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

G. Alistair Watson

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

Publish with us

Policies and ethics

Search

Navigation