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Reducing the Uncertainty When Approximating the Solution of ODEs

  • Wayne H. Enright
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 377)

Abstract

One can reduce the uncertainty in the quality of an approximate solution of an ordinary differential equation (ODE) by implementing methods which have a more rigorous error control strategy and which deliver an approximate solution that is much more likely to satisfy the expectations of the user. We have developed such a class of ODE methods as well as a collection of software tools that will deliver a piecewise polynomial as the approximate solution and facilitate the investigation of various aspects of the problem that are often of as much interest as the approximate solution itself. We will introduce measures that can be used to quantify the reliability of an approximate solution and discuss how one can implement methods that, at some extra cost, can produce very reliable approximate solutions and therefore significantly reduce the uncertainty in the computed results.

Keywords

Numerical methods initial value problems ODEs reliable methods defect control 

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Copyright information

© IFIP International Federation for Information Processing 2012

Authors and Affiliations

  • Wayne H. Enright
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoCanada

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