The Dangers of Rounding Errors for Simulations and Analysis of Nonlinear Circuits and Systems?and How to Avoid Them

Abstract

Due to rounding errors results obtained by numerical simulations of nonlinear systems may be unreliable. It is however possible to carry out the computations in such a way that the results obtained are rigorous. In this paper several tools based on interval analysis are presented. Methods for computing trajectories, techniques for finding accurate enclosures of attractors, interval operators for proving the existence of fixed points and periodic orbits, and methods for proving the existence of nontrivial symbolic dynamics, are described. Computational techniques are illustrated by performing validated numerical analysis of the Hénon map and the Chua's circuit.