Monotone Waveform Relaxation for Systems of Nonlinear Differential-Algebraic Equations

Authors:
Yao-Lin Jiang;Omar Wing
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 4

Waveform relaxation methods for periodic differential-functional systems

Journal of Computational and Applied Mathematics
Convergence analysis of waveform relaxation methods for neutral differential-functional systems

Journal of Computational and Applied Mathematics
Waveform relaxation and comparison methods for multipoint boundary value problems

Computers & Mathematics with Applications
Nonnegative solutions of fractional functional differential equations

Computers & Mathematics with Applications

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Abstract

We present a monotone waveform relaxation algorithm which produces very tight upper and lower bounds of the transient response of a class of systems described by nonlinear differential-algebraic equations (DAEs) that satisfy certain Lipschitz conditions. The choice of initial iteration is critical and we give two methods of finding it. We show that the class of systems in which monotone convergence of waveform relaxation is possible is actually larger than previously reported. Numerical experiments are given to confirm the monotonicity of convergence of the algorithm.