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Zusatztext ...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 parallel numerical 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 of parallel methods for this class of problems. Ken Jackson, SIAM Review, Vol. 39 No. 2, June 1997 Klappentext As scientific technology becomes increasingly more sophisticated, numerical analysts, mathematicians, and engineers have to solve larger and larger problems, necessitating the use of parallel computers. This book presents an up-to-date exposition of the current state of the art of numerical methods for solving ordinary equations in a parallel computing environment. Although the main focus is on problems of initial value type, boundary value problems and partial differentiation equations are also covered. Other chapters are devoted to the parallel solution of linear systems of equation, existing sequential differential equation methods, and the behavior of a parallel code based on wave relaxation. Zusammenfassung 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. 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 ...
