Skip to main content

A revised mesh refinement strategy for newton’s method applied to nonlinear two-point boundary value problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 679)

Abstract

The objective of this paper is the development of a mesh refinement technique for applying Newton’s method to the solution of nonlinear two-point boundary value problems. The process represents a significant improvement on an earlier approach both in its general applicability and in its numerical performance. This is demonstrated by several reported numerical examples.

Keywords

  • Coarse Grid
  • Truncation Error
  • Final Grid
  • Mesh Refinement
  • Newton Iteration

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 work was supported by the National Science Foundation under grant number MCS76-09215.

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. E. L. Allgower and S. F. McCormick, A phenomenon concerning Newton’s method for boundary value problems and its application to mesh refinement, Numer. Math., to appear.

    Google Scholar 

  2. E. L. Allgower, S. F. McCormick, and D. V. Pryor, A general mesh independence principle for Newton’s method applied to second order boundary value problems, submitted for publication.

    Google Scholar 

  3. E. L. Allgower, On a discretization of y″ + λyk=0, Topics in Numerical Analysis II, ed. J. J. H. Miller, New York, Academic Press, (1975) 1–15.

    CrossRef  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

McCormick, S.F. (1978). A revised mesh refinement strategy for newton’s method applied to nonlinear two-point boundary value problems. In: Ansorge, R., Törnig, W. (eds) Numerical Treatment of Differential Equations in Applications. Lecture Notes in Mathematics, vol 679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067863

Download citation

  • DOI: https://doi.org/10.1007/BFb0067863

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08940-7

  • Online ISBN: 978-3-540-35715-5

  • eBook Packages: Springer Book Archive