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Zbl 1001.94058
Jiang, Yao-Lin; Chen, Richard M.M.; Wing, Omar
Convergence analysis of waveform relaxation for nonlinear differential-algebraic equations of index one. (English)
[J] IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 47, No.11, 1639-1645 (2000). ISSN 1057-7122

Summary: We give a new and simple convergence theorem on the waveform relaxation (WR) solution for a system of nonlinear differential-algebraic equations of index one. We show that if the norms of certain matrices derived from the Jacobians of the system functions are less than one, then the WR solution converges. The new sufficient condition includes previously reported conditions as special cases. Examples are given to confirm the theoretical analysis.

MSC 2000:: *94C05 Analytic circuit theory
65L80 Methods for differential-algebraic equations

Keywords: circuit simulation; convergence analysis; waveform relaxation solution; nonlinear differential-algebraic equations

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