Title :
Convergence analysis of waveform relaxation for nonlinear differential-algebraic equations of index one
Author :
Jiang, Yao-Lin ; Chen, Richard M M ; Wing, Omar
Author_Institution :
Inst. of Inf. & Syst. Sci., Xi´´an Jiaotong Univ., China
fDate :
11/1/2000 12:00:00 AM
Abstract :
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
Keywords :
circuit simulation; convergence of numerical methods; iterative methods; nonlinear differential equations; nonlinear network analysis; Jacobians; convergence analysis; nonlinear differential-algebraic equations; system functions; waveform relaxation; Analytical models; Convergence; Councils; Differential equations; Electronic circuits; Jacobian matrices; Nonlinear equations; Sufficient conditions; Transient analysis; Very large scale integration;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
