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

Journal article
Authors Benjamin Kehlet
Anders Logg
Published in Numerical Algorithms
Volume 76
Issue 1
Pages 191-210
ISSN 1017-1398
Publication year 2017
Published at Department of Mathematical Sciences
Pages 191-210
Language en
Keywords A posteriori, Computability, Finite element, High accuracy, High order, High precision, Long-time integration, Lorenz, Probabilistic error propagation, Time-stepping, Van der Pol
Subject categories Mathematics


© 2016, The Author(s). 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.

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