Skip to main content
SpringerLink
Log in

An adaptive implementation of interpolation methods for boundary value ordinary differential equations

  • Part II Numerical Mathematics
  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

Various interpolation-based schemes are used to construct a variable order algorithm with local error control for the numerical solution of two-point boundary value problems. Results of computational experiments are presented to demonstrate the empirical relationship between prescribed local error and the resultant global error in the computed solution.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Lentini and V. Pereyra,A variable order finite difference method for nonlinear multi-point boundary value problems, Math. Comp., 28 (1974).

  2. U. Ascher,Solving boundary-value problems with a spline-collocation code, J. Comp. Physics, 34 (1980).

  3. B. Childs (ed.),Codes for Boundary-Value Problems in Ordinary Differential Equations, Lecture Notes in Computer Science 76, Springer-Verlag, New York (1979).

    Google Scholar 

  4. J. Ortega and W. C. Rheinboldt,Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, N.Y. 1970.

    Google Scholar 

  5. R. P. Tewarson and S. Gupta,Improving the accuracy of finite difference methods for solving boundary value ordinary differential equations, BIT 22 (1982), 353–360.

    Google Scholar 

  6. R. P. Tewarson,On the use of splines for the numerical solution of non-linear two-point boundary value problems, BIT 20 (1980), 223–232.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied Mathematics and Statistics Department, State University of New York, 11794, Stony Brook, N.Y., U.S.A.

    R. P. Tewarson & N. S. Huslak

Authors
  1. R. P. Tewarson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. S. Huslak
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by NIH Grant No. AM17593.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tewarson, R.P., Huslak, N.S. An adaptive implementation of interpolation methods for boundary value ordinary differential equations. BIT 23, 382–387 (1983). https://doi.org/10.1007/BF01934466

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01934466

Keywords

Search

Navigation