Parallel and Sequential Methods for Ordinary Differential Equations by Kevin Burrage

Parallel and Sequential Methods for Ordinary Differential Equations

byKevin Burrage

Hardcover | April 30, 1999

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This book presents an up-to-date exposition of the current `state of the art' of numerical methods for solving ordinary differential equations in a parallel computing environment. Although the main focus is on problems of initial value type, consideration will also be given to boundary valueproblems and partial differential equations. Furthermore, because linear algebra is an important component of the solution of differential equations, a complete chapter is devoted to the parallel solution of linear systems of equations. In addition to presenting an overview of parallel computing ingeneral, two chapters are devoted to a summary of existing sequential differential equation methods. The parallel techniques discussed include parallelism across the method, parallelism across the step, parallelism across the system, and dynamic iteration. The book concludes with a chapter on thebehaviour of a parallel code based on waveform relaxation.This comprehensive book is unique in its content and provides a balance between theoretical and practical issues by providing general frameworks in which to study parallel methods.

About The Author

Kevin Burrage is at University of Queensland, Brisbane.

Details & Specs

Title:Parallel and Sequential Methods for Ordinary Differential EquationsFormat:HardcoverDimensions:462 pages, 9.21 × 6.14 × 1.18 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198534329

ISBN - 13:9780198534327

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Table of Contents

1. Aspects of parallel computing2. An introduction to sequential ODE methods3. Order and stability - a general framework4. Parallel linear algebra5. Direct methods for ODEs6. Diverse approaches to parallelism7. Waveform relaxation techniques8. Discrete waveform methods9. Implementation of waveform algorithmsList of symbolsReferences

Editorial Reviews

...written at a level that should be accessible to most engineers and scientists familiar with numerical methods for ODEs and graduate, or senior undergraduate, students specializing in numerical computing. ... it is an ideal starting point for anyone interested in learning about parallelnumerical methods for IVPs for ODEs as well as a valuable reference for established researchers in the area . . . Although several excellent books on numerical methods for IVPs for ODEs have appeared in the last few years, Burrage's monograph is unique in its breadth and depth of discussion ofparallel methods for this class of problems. Ken Jackson, SIAM Review, Vol. 39 No. 2, June 1997