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

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.

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