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Numerical Algorithms

, Volume 76, Issue 1, pp 191–210 | Cite as

A posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations

  • Benjamin Kehlet
  • Anders Logg
Open Access
Original Paper

Abstract

We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretization errors with a new term accounting for the propagation of numerical round-off errors, showing that the accumulated round-off error is inversely proportional to the square root of the step size. As a consequence, the numeric precision eventually sets the limit for the pointwise computability of accurate solutions of any ODE. The theoretical results are supported by numerically computed solutions and error estimates for the Lorenz system and the van der Pol oscillator.

Keywords

Computability High precision High order High accuracy Probabilistic error propagation Long-time integration Finite element Time-stepping A posteriori Lorenz Van der Pol 

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Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.University of OsloOsloNorway
  2. 2.Simula Research LaboratoryLysakerNorway
  3. 3.Department of Mathematical SciencesChalmers University of TechnologyGothenburgSweden
  4. 4.University of GothenburgGothenburgSweden

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