Files in this item
|(no description provided)|
|Title:||Waveform methods for ordinary differential equations|
|Doctoral Committee Chair(s):||Gear, C.W.|
|Department / Program:||Computer Science|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
|Rights Information:||Copyright 1990 Juang, Fen-Lien|
|Date Available in IDEALS:||2011-05-07|
|Identifier in Online Catalog:||AAI9021701|