Parallel methods for the numerical solution of ordinary differential equations

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Tam, Hon Wah

Contributors dc:contributor

• Skeel, Robert D.

• Computer Science

Statement dc:rights

• Copyright 1989 Tam, Hon Wah

Language dc:language

eng

Identifier

AAI8924952
(UMI)AAI8924952

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/21272