Title :
Waveform relaxation of nonlinear second-order differential equations
Author :
Jiang, Yao-Lin ; Chen, Richard M M ; Wing, Omar
Author_Institution :
Sch. of Sci., Xi´´an Jiaotong Univ., China
fDate :
11/1/2001 12:00:00 AM
Abstract :
In this paper, we give a simple theorem on the waveform relaxation (WR) solution for a system of nonlinear second-order differential equations. It is shown that if the norm of certain matrices derived from the Jacobians of the system equations is less than one, then the WR solution converges. It is also the first time that a convergence condition has been obtained for this general kind of nonlinear system in the WR literature. Numerical experiments are provided to confirm the theoretical analysis
Keywords :
Jacobian matrices; circuit simulation; convergence of numerical methods; iterative methods; nonlinear differential equations; nonlinear network analysis; parallel processing; transient analysis; Jacobians; circuit simulation; convergence condition; iterative process; matrix norm; nonlinear electronic circuits; nonlinear second-order differential equations; parallel processing; system equations; transient analysis; waveform relaxation solution; Circuit simulation; Differential equations; Electronic circuits; Iterative algorithms; Jacobian matrices; Nonlinear equations; Nonlinear systems; Parallel processing; Transient analysis; Very large scale integration;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
