Parallel and Sequential Methods for Ordinary Differential Equations

Erscheinungsjahr 1997
ISBN: 978-0-19-853432-7
Verlag: OUP Oxford

Buch, Englisch, 462 Seiten, Print PDF, Format (B × H): 157 mm x 235 mm, Gewicht: 899 g

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 value problems 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 in general, 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 the behaviour 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.

Autoren/Hrsg.

Burrage, Kevin

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

- 1.: Aspects of parallel computing

- 2.: An introduction to sequential ODE methods

- 3.: Order and stability - a general framework

- 4.: Parallel linear algebra

- 5.: Direct methods for ODEs

- 6.: Diverse approaches to parallelism

- 7.: Waveform relaxation techniques

- 8.: Discrete waveform methods

- 9.: Implementation of waveform algorithms

- List of symbols

- References