Waveform relaxation of nonlinear second-order differential equations

Authors
Jiang, YL Chen, RMM Wing, O
Citation
Yl. Jiang et al., Waveform relaxation of nonlinear second-order differential equations, IEEE CIRC-I, 48(11), 2001, pp. 1344-1347
Citations number
12
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS
ISSN journal
10577122 → ACNP
Volume
48
Issue
11
Year of publication
2001
Pages
1344 - 1347
Database
ISI
SICI code
1057-7122(200111)48:11<1344:WRONSD>2.0.ZU;2-B
Abstract
In this paper, we give a simple theorem on the waveform relaxation (WR) sol ution for a system of nonlinear second-order differential equations. It is shown that if the norm of certain matrices derived from the Jacobians of th e 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 gener al kind of nonlinear systems in the WR literarture. Numerical experiments a re provided to confirm the theoretical analysis.