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Gear, C.W. Juang, Fen-Lien 2011-05-07T12:20:50Z 2011-05-07T12:20:50Z 10000-01-01 1990 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. Made available in DSpace on 2011-05-07T12:20:50Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9021701.pdf: 4344986 bytes, checksum: e461dda96572acdee0c6872d7f604859 (MD5) Previous issue date: 1990 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:39:53Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:16:56-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9021701 (UMI)AAI9021701 http://hdl.handle.net/2142/19855 eng Copyright 1990 Juang, Fen-Lien Computer Science Waveform methods for ordinary differential equations text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.