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Chapter 6

On the Convergence of Asynchronous Waveform Relaxation Algorithms for Differential Equations

J.M. Bahi, J.-C. Miellou and M. El-Kyal

IUT de Belfort, Belfort, France

doi:10.4203/csets.9.6

J.M. Bahi, J.-C. Miellou, M. El-Kyal, "On the Convergence of Asynchronous Waveform Relaxation Algorithms for Differential Equations", in B.H.V. Topping, (Editor), "Computational Mechanics using High Performance Computing", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 6, pp 117-133, 2002. doi:10.4203/csets.9.6

Abstract

The aim of this Chapter is to prove the superlinear convergence of asynchronous waveform relaxation (AWR) methods applied to a system of nonlinear ordinary differential equations (ODEs). This study is based on the technique of nested sets. It enables the specification of the kind of convergence using the theory introduced by Bertsekas and Tsitsiklis. A computational mechanics based example is presented.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Computational Science, Engineering & Technology Series ISSN 1759-3158 CSETS: 9 COMPUTATIONAL MECHANICS USING HIGH PERFORMANCE COMPUTING Edited by: B.H.V. Topping Chapter 6 On the Convergence of Asynchronous Waveform Relaxation Algorithms for Differential Equations J.M. Bahi, J.-C. Miellou and M. El-Kyal IUT de Belfort, Belfort, France doi:10.4203/csets.9.6 purchase the full-text of this chapter Full Bibliographic Reference for this chapter J.M. Bahi, J.-C. Miellou, M. El-Kyal, "On the Convergence of Asynchronous Waveform Relaxation Algorithms for Differential Equations", in B.H.V. Topping, (Editor), "Computational Mechanics using High Performance Computing", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 6, pp 117-133, 2002. doi:10.4203/csets.9.6 Abstract The aim of this Chapter is to prove the superlinear convergence of asynchronous waveform relaxation (AWR) methods applied to a system of nonlinear ordinary differential equations (ODEs). This study is based on the technique of nested sets. It enables the specification of the kind of convergence using the theory introduced by Bertsekas and Tsitsiklis. A computational mechanics based example is presented. purchase the full-text of this chapter (price £20) go to the previous chapter go to the next chapter return to the table of contents return to the book description purchase this book (price £90 +P&P)
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