Waveform relaxation of nonlinear second-order differential equations

Yao Lin Jiang; Richard M.M. Chen; Omar Wing

doi:10.1109/81.964425

Waveform relaxation of nonlinear second-order differential equations

Yao Lin Jiang
, Richard M.M. Chen
, Omar Wing

School of Mathematics and Statistics

City University of Hong Kong
Chinese University of Hong Kong

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 is obtained for this general kind of nonlinear systems in the WR literature. Numerical experiments are provided to confirm the theoretical analysis.

Original language	English
Pages (from-to)	1344-1347
Number of pages	4
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	48
Issue number	11
DOIs	https://doi.org/10.1109/81.964425
State	Published - Nov 2001

Keywords

Circuit simulation
Parallel processing
Second-order differential equations
Waveform relaxation

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10.1109/81.964425

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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 is obtained for this general kind of nonlinear systems in the WR literature. Numerical experiments are provided to confirm the theoretical analysis.",

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KW - Parallel processing

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Waveform relaxation of nonlinear second-order differential equations

Abstract

Keywords

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