University of Illinois Urbana-Champaign

Waveform methods for ordinary differential equations

Juang, Fen-Lien

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https://hdl.handle.net/2142/19855

Description

Title
Waveform methods for ordinary differential equations
Author(s)
Juang, Fen-Lien
Issue Date
1990
Doctoral Committee Chair(s)
Gear, C.W.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
  • The traditional approach for solving large dynamical systems is time consuming. Waveform method, an iterative technique for solving systems of differential equations, can be used to reduce the processing time. Waveform method has been shown to converge superlinearly on finite intervals. In this thesis, a measure of speed of convergence is defined and is used to compare the value of different waveform methods. This measure is the rate of increase of order of accuracy.
  • The speed of the waveform Gauss-Seidel method depends on the numbering of the equations. The numbering of the equations corresponds to a numbering of the directed graph specifying the coupling relations among all equations. We show how to compute the rate of order increase from the structure of the numbered graph and hence the optimum numbering, that is, the one which maximizes the speed of convergence. Finally, in a variety of numerical experiments, conducted on a SUN 3/60, we demonstrate the different speed of convergence corresponds to different numbering and the effectiveness of the waveform Gauss-Seidel method for large sparse systems.
Type of Resource
text
Permalink
http://hdl.handle.net/2142/19855
Copyright and License Information
Copyright 1990 Juang, Fen-Lien

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Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Computer Science
Dissertations and Theses from the Dept. of Computer Science