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
Probabilistic error propagation
Methods
High precision
High order
One-Step
Computability
Long-time
Odes
Computational Uncertainty Principle
High accuracy
Author
B. Kehlet
University of Oslo
Simula Research Laboratory
Anders Logg
University of Gothenburg
Chalmers, Mathematical Sciences
Numerical Algorithms
1017-1398 (ISSN) 15729265 (eISSN)
Vol. 76 1 191-210Subject Categories
Mathematics
DOI
10.1007/s11075-016-0250-4