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.
Methods
Long-time
High accuracy
Computability
High order
High precision
Odes
Probabilistic error propagation
One-Step
Computational Uncertainty Principle
Adaptive Galerkin Methods
Author
B. Kehlet
Simula Research Laboratory
Universitetet i Oslo
Anders Logg
Chalmers, Mathematical Sciences
University of Gothenburg
Numerical Algorithms
1017-1398 (ISSN)
Vol. 76 1 191-210Subject Categories (SSIF 2011)
Mathematics
DOI
10.1007/s11075-016-0250-4