Explicit approximation methods for initial-value problems

 

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dc.contributor.advisor Parkyn, D G en_ZA
dc.contributor.author Joubert, Gerhard Robert en_ZA
dc.date.accessioned 2015-04-02T13:56:42Z
dc.date.available 2015-04-02T13:56:42Z
dc.date.issued 1969 en_ZA
dc.identifier.citation Joubert, G. 1969. Explicit approximation methods for initial-value problems. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/12639
dc.description.abstract Explicit difference approximations of parabolic initial boundary value problems are usually stable only if a difference grid with a limited time-step is used. By considering the one-dimensional diffusion equation as an example, it is shown in the following work that simple smoothing formulas can be constructed which, when applied to solutions computed with unstable explicit difference equations, result in stable approximations of the solution of the differential equation. Such computational procedures can be expressed as explicit difference analogues of the problem considered. Conversely, explicit difference approximations, which need not be defined for all points of the difference grid but must be stable for the specific grid used, can be written as non-unique combinations of an explicit difference approximation, which need not be stable, and a smoothing formula. By appropriate choice of these explicit difference approximations and smoothing formulas this procedure will be defined for all grid points. This new technique thus has the advantage that explicit difference approximations with comparatively weak stability requirements and/or small truncation errors can be used in practice. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.title Explicit approximation methods for initial-value problems en_ZA
dc.type Doctoral 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 Doctoral
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Joubert, G. R. (1969). <i>Explicit approximation methods for initial-value problems</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/12639 en_ZA
dc.identifier.chicagocitation Joubert, Gerhard Robert. <i>"Explicit approximation methods for initial-value problems."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1969. http://hdl.handle.net/11427/12639 en_ZA
dc.identifier.vancouvercitation Joubert GR. Explicit approximation methods for initial-value problems. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1969 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/12639 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Joubert, Gerhard Robert AB - Explicit difference approximations of parabolic initial boundary value problems are usually stable only if a difference grid with a limited time-step is used. By considering the one-dimensional diffusion equation as an example, it is shown in the following work that simple smoothing formulas can be constructed which, when applied to solutions computed with unstable explicit difference equations, result in stable approximations of the solution of the differential equation. Such computational procedures can be expressed as explicit difference analogues of the problem considered. Conversely, explicit difference approximations, which need not be defined for all points of the difference grid but must be stable for the specific grid used, can be written as non-unique combinations of an explicit difference approximation, which need not be stable, and a smoothing formula. By appropriate choice of these explicit difference approximations and smoothing formulas this procedure will be defined for all grid points. This new technique thus has the advantage that explicit difference approximations with comparatively weak stability requirements and/or small truncation errors can be used in practice. DA - 1969 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1969 T1 - Explicit approximation methods for initial-value problems TI - Explicit approximation methods for initial-value problems UR - http://hdl.handle.net/11427/12639 ER - en_ZA


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