The stability of linear operators

 

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dc.contributor.advisor Kotzé, W en_ZA
dc.contributor.author Colburn, Hugh Edwin Geoffrey en_ZA
dc.date.accessioned 2016-03-21T19:05:56Z
dc.date.available 2016-03-21T19:05:56Z
dc.date.issued 1970 en_ZA
dc.identifier.citation Colburn, H. 1970. The stability of linear operators. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/18034
dc.description.abstract In the approximation and solution of both ordinary and partial differential equations by finite difference equations, it is well-known that for different ratios of the time interval to the spatial intervals widely differing solutions are obtained. This problem was first attacked by John von Neumann using Fourier analysis. It has also been studied in the context of the theory of semi-groups of operators. It seemed that the problem could be studied with profit if set in a more abstract structure. The concepts of the stability of a linear operator on a (complex) Banach space and the stability of a Banach sub-algebra of operators were formed in an attempt to generalize the matrix 2 theorems of H.O. Kreiss as applied to the L² stability problem. Chapter 1 deals with the stability and strict stability of linear operators. The equivalence of stability and convergence is discussed in Chapter 2 and special cases of the Equivalence Theorem are considered in Chapters 3 and 4. In Chapter 5 a brief account of the theory of discretizations is given and used to predict instability in non-linear algorithms. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Applied Mathematics en_ZA
dc.title The stability of linear operators en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Colburn, H. E. G. (1970). <i>The stability of linear operators</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/18034 en_ZA
dc.identifier.chicagocitation Colburn, Hugh Edwin Geoffrey. <i>"The stability of linear operators."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1970. http://hdl.handle.net/11427/18034 en_ZA
dc.identifier.vancouvercitation Colburn HEG. The stability of linear operators. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1970 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/18034 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Colburn, Hugh Edwin Geoffrey AB - In the approximation and solution of both ordinary and partial differential equations by finite difference equations, it is well-known that for different ratios of the time interval to the spatial intervals widely differing solutions are obtained. This problem was first attacked by John von Neumann using Fourier analysis. It has also been studied in the context of the theory of semi-groups of operators. It seemed that the problem could be studied with profit if set in a more abstract structure. The concepts of the stability of a linear operator on a (complex) Banach space and the stability of a Banach sub-algebra of operators were formed in an attempt to generalize the matrix 2 theorems of H.O. Kreiss as applied to the L² stability problem. Chapter 1 deals with the stability and strict stability of linear operators. The equivalence of stability and convergence is discussed in Chapter 2 and special cases of the Equivalence Theorem are considered in Chapters 3 and 4. In Chapter 5 a brief account of the theory of discretizations is given and used to predict instability in non-linear algorithms. DA - 1970 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1970 T1 - The stability of linear operators TI - The stability of linear operators UR - http://hdl.handle.net/11427/18034 ER - en_ZA


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