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.

Methods

Long-time

High accuracy

Computability

High order

High precision

Odes

Probabilistic error propagation

One-Step

Computational Uncertainty Principle

Adaptive Galerkin Methods

Författare

B. Kehlet

Simula Research Laboratory

Universitetet i Oslo

Anders Logg

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Numerical Algorithms

1017-1398 (ISSN)

Vol. 76 191-210

Ämneskategorier

Matematik

DOI

10.1007/s11075-016-0250-4