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

Adaptive Galerkin Methods

High precision

Long-time

Computational Uncertainty Principle

Methods

High accuracy

High order

Odes

One-Step

Probabilistic error propagation

Computability

Author

B. Kehlet

University of Oslo

Simula Research Laboratory

Anders Logg

University of Gothenburg

Chalmers, Mathematical Sciences

Numerical Algorithms

1017-1398 (ISSN)

Vol. 76 1 191-210

Subject Categories

Mathematics

DOI

10.1007/s11075-016-0250-4

More information

Latest update

9/6/2018 1