Skip to main content

Implicit methods for implicit differential equations

  • Conference paper
  • First Online:
Conference on the Numerical Solution of Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 109))

Abstract

Quadrature methods are used to obtain numerical solutions of certain systems of implicit differential equations. Several examples indicate the range of application of the methods.

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

Access this chapter

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. Butcher, J. C.: Implicit Runge-Kutta processes. Math.Comp. 18, 50–64(1964).

    Article  MathSciNet  MATH  Google Scholar 

  2. Collatz, L.: The numerical treatment of differential equations. Berlin: Springer-Verlag 1960.

    Book  MATH  Google Scholar 

  3. Cooper, G. J.: A class of single step methods for systems of nonlinear differential equations. Math. Comp. 21, 597–610(1967).

    Article  MathSciNet  MATH  Google Scholar 

  4. —: Interpolation and quadrature methods for ordinary differential equations. Math. Comp. 22, 69–76(1968).

    Article  MathSciNet  MATH  Google Scholar 

  5. Murray, F. J., and K. S. Miller: Existence theorems for ordinary differential equations. New York: New York University Press 1954.

    MATH  Google Scholar 

  6. Verner, J. H.: The order of some implicit Runge-Kutta methods. Num. Math. 13, 14–23(1969).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

J. Li. Morris

Rights and permissions

Reprints and permissions

Copyright information

© 1969 Springer-Verlag

About this paper

Cite this paper

Verner, J.H. (1969). Implicit methods for implicit differential equations. In: Morris, J.L. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060038

Download citation

  • DOI: https://doi.org/10.1007/BFb0060038

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04628-8

  • Online ISBN: 978-3-540-36158-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics