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

B. Kehlet ; Anders Logg (Institutionen för matematiska vetenskaper)
Numerical Algorithms (1017-1398). Vol. 76 (2017), 1, p. 191-210.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Computability, High precision, High order, High accuracy, Probabilistic error propagation, Long-time, Computational Uncertainty Principle, Adaptive Galerkin Methods, One-Step, Methods, Odes



Denna post skapades 2017-09-12.
CPL Pubid: 251849

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

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Matematik

Chalmers infrastruktur