AuthorsB. Kehlet and A. Logg
TitleA posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations
AfilliationScientific Computing
Publication TypeJournal Article
Year of Publication2017
JournalNumerical Algorithms
Date Published09/2017
Publisher Springer

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 discretisation
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.