Skip to main content

One-step methods with adaptive stability functions for the integration of differential equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 333)

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   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.95
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

  • Calahan, D.A. [1968]: A stable, accurate method of numerical integration for non-linear systems, Proc. IEEE 56, 744.

    CrossRef  Google Scholar 

  • Dahlquist, G.G. [1963]: A special stability problem for linear multistep problems, BIT 3, 27.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Houwen, P.J. van der [1972a]: Explicit and semi-implicit Runge-Kutta formulas for the integration of stiff equations, Report TW 132/72, Mathematisch Centrum, Amsterdam. [1972b]: Explicit Runge-Kutta formulas with increased stability boundaries, Numerische Mathematik (to appear).

    Google Scholar 

  • Lapidus, L. and J.H. Seinfeld [1971]: Numerical solution of ordinary differential equations, Academic Press, New York.

    MATH  Google Scholar 

  • Liniger, W. and R.A. Willoughby [1970]: Efficient integration methods for stiff systems of ordinary differential equations, SIAM J., Numer. Anal. 7, 47.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Robertson, H.H. [1967]: The solution of a set of reaction rate equations in "Numerical Analysis", (J. Walsh, ed.), Thompson Book Co., Washington.

    Google Scholar 

  • Rosenbrock, H.H. [1963]: Some general implicit processes for the numerical solution of differential equations, Comput. J. 5, 329.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

van der Houwen, P.J. (1973). One-step methods with adaptive stability functions for the integration of differential equations. In: Ansorge, R., Törnig, W. (eds) Numerische, insbesondere approximationstheoretische Behandlung von Funktionalgleichungen. Lecture Notes in Mathematics, vol 333. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060695

Download citation

  • DOI: https://doi.org/10.1007/BFb0060695

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06378-0

  • Online ISBN: 978-3-540-46986-5

  • eBook Packages: Springer Book Archive