BIT Numerical Mathematics

, Volume 20, Issue 1, pp 67–82 | Cite as

Some experiments with interval methods for two-point boundary-value problems in ordinary differential equations

  • L. Fox
  • M. R. Valenca
Part II Numerical Mathematics

Abstract

Methods of interval mathematics are used to find upper and lower bounds for the solution of two-point boundary-value problems at discrete mesh points. They include interval versions of shooting and of finite-difference techniques for linear and non-linear differential equations of second order, and of finite-difference methods for Sturm-Liouville eigenvalue problems.

Good results are obtained whenever the difficulties of dependency-width can be avoided, and particularly for the finite-difference method when the associated matrix is anM matrix.

Keywords

Differential Equation Lower Bound Ordinary Differential Equation Computational Mathematic Mesh Point 

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Copyright information

© BIT Foundations 1980

Authors and Affiliations

  • L. Fox
    • 1
  • M. R. Valenca
    • 1
  1. 1.Computing LaboratoryOxford UniversityOxfordEngland

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