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Title:Parallel methods for the numerical solution of ordinary differential equations
Author(s):Tam, Hon Wah
Doctoral Committee Chair(s):Skeel, Robert D.
Department / Program:Computer Science
Discipline:Computer Science
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Computer Science
Abstract:We study time parallelism for the numerical solution of nonstiff ordinary differential equations. Stability and accuracy are the two main considerations in deriving good numerical o.d.e. methods. However, existing parallel methods have poor stability properties in that their stability regions are smaller than those of good sequential methods of the same order. In this thesis we present a precise understanding of how stability limits the potential of parallelism in o.d.e.'s. We propose a fairly specific approach to construct good parallel methods--we consider zero-stable parallel methods whose stability polynomials are perfect powers of those of simple methods with good stability regions. Based on this approach we derive new efficient parallel methods. The proposed families of block methods have stability regions which do not change as the order increases. These new methods have much better stability properties than the Adams PECE methods of the same order. The above perfect power stability polynomial approach can also be extended to multi-block methods.
Issue Date:1989
Rights Information:Copyright 1989 Tam, Hon Wah
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI8924952
OCLC Identifier:(UMI)AAI8924952

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