A general approach to waveform relaxation solutions of nonlinear differential-algebraic equations: the continuous-time and discrete-time cases

Author

Jiang, Yao-Lin

Author_Institution

Sch. of Sci., Xi´´an Jiaotong Univ., China

Volume

51

Issue

9

fYear

2004

Firstpage

1770

Lastpage

1780

Abstract

For a general class of nonlinear differential-algebraic equations of index one, we develop and unify a convergence theory on waveform relaxation (WR). Convergence conditions are achieved for the cases of continuous-time and discrete-time WR approximations. Most of known convergence results in this field can be easily derived from the new theory established here.

Keywords

circuit simulation; continuous time systems; convergence of numerical methods; discrete time systems; iterative methods; nonlinear differential equations; polynomial approximation; waveform analysis; circuit simulation; continuous-time case; continuous-time waveform relaxation iteration; convergence conditions; convergence theory; discrete-time case; discrete-time waveform relaxation iteration; nonlinear differential-algebraic equations; numerical algorithms; waveform relaxation solutions; Circuit simulation; Clustering algorithms; Computer aided software engineering; Convergence of numerical methods; Delay; Differential equations; Jacobian matrices; Nonlinear equations; Personal communication networks; Workstations; Continuous-time and discrete-time waveform relaxation; DAEs; WR; circuit simulation; convergence conditions; differential-algebraic equations; iterations; numerical algorithms;

fLanguage

English

Journal_Title

Circuits and Systems I: Regular Papers, IEEE Transactions on

Publisher

ieee

ISSN

1549-8328

Type

jour

DOI

10.1109/TCSI.2004.834503

Filename

1333226