Title :
A general approach to waveform relaxation solutions of nonlinear differential-algebraic equations: the continuous-time and discrete-time cases
Author_Institution :
Sch. of Sci., Xi´´an Jiaotong Univ., China
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;
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
DOI :
10.1109/TCSI.2004.834503
