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oai:www.ideals.illinois.edu:2142/21587 2023-07-10 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Gear, C.W. Keiper, Jerry Bruce 2011-05-07T13:13:05Z 2011-05-07T13:13:05Z 10000-01-01 1989 We study the numerical solution of Hessenberg form differential algebraic equations by variable stepsize generalized backward difference formulae (GBDF). GBDF methods of sufficiently high order are shown to converge for problems of index two, three, or four. The proof techniques developed are not sufficiently powerful to show convergence for index five problems. In addition, we perform very high precision numerical experiments on problems of index two, three, four, and five, using the classical six step backward difference formula. The experiments confirm the analysis regarding the error behavior of the index two and three problems, but suggest that the analysis of the index four problem is too pessimistic. It appears from the experiments that index five problems can also be solved by GBDF methods. Made available in DSpace on 2011-05-07T13:13:05Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9010913.pdf: 3119596 bytes, checksum: ac24d3de4b53556d5d1a07ee84e102ea (MD5) Previous issue date: 1989 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:51:47Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:23:49-05:00 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 AAI9010913 (UMI)AAI9010913 http://hdl.handle.net/2142/21587 eng Copyright 1989 Keiper, Jerry Bruce Computer Science Generalized BDF methods applied to Hessenberg form DAEs text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.