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

Author

Galias, Zbigniew

Author_Institution

Dept. of Electr. Eng., AGH Univ. of Sci. & Technol., Krakow, Poland

Volume

13

Issue

3

fYear

2013

fDate

thirdquarter 2013

Firstpage

35

Lastpage

52

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.

Keywords

Chua´s circuit; Henon mapping; circuit simulation; electronics packaging; nonlinear network analysis; numerical analysis; Chua´s circuit; Hénon map; computational technique; computing trajectory; enclosure; interval analysis; nonlinear circuit; nontrivial symbolic dynamics; numerical simulation; periodic orbit; rounding error; Error analysis; Nonlinear systems; Numerical analysis; Simulation; Steady-state; Vectors;

fLanguage

English

Journal_Title

Circuits and Systems Magazine, IEEE

Publisher

ieee

ISSN

1531-636X

Type

jour

DOI

10.1109/MCAS.2013.2271444

Filename

6585769