A posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations
Artikel i vetenskaplig tidskrift, 2017

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.

High order

Probabilistic error propagation

One-Step

Odes

Adaptive Galerkin Methods

Methods

High accuracy

Long-time

High precision

Computational Uncertainty Principle

Computability

Författare

B. Kehlet

Universitetet i Oslo

Simula Research Laboratory

Anders Logg

Göteborgs universitet

Chalmers, Matematiska vetenskaper

Numerical Algorithms

1017-1398 (ISSN)

Vol. 76 191-210

Ämneskategorier

Matematik

DOI

10.1007/s11075-016-0250-4