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