Numerical solutions of diffusion-type equations

dc.contributor.advisorChilds, S. Bart
dc.contributor.committeeMemberHedgcoxe, Pat G.
dc.contributor.committeeMemberBannerot, Richard B.
dc.contributor.committeeMemberHubbard, Martin G.
dc.creatorBryan, John Loyd
dc.date.accessioned2022-10-06T16:17:32Z
dc.date.available2022-10-06T16:17:32Z
dc.date.issued1969
dc.description.abstractA method of obtaining numerical solutions of a general class of boundary-value problems governed by the two-dimensional diffusion equation is investigated. The method employs a partial discretization of independent variables to reduce the problem of partial differential equations to a sequence of related boundary-value problems governed by a system of linear second-order ordinary differential equations. The generality of the method is demonstrated by applications to example problems involving both regular and irregular boundaries with boundary conditions of a general type. Application of separation of variables techniques to obtain closed-form solutions of a certain class of problems is presented and the results are used to indicate the accuracy of the method. An investigation into the stability characteristics of the resulting system of ordinary differential equations is also presented. It is concluded that the method appears to show promise as an easily implemented numerical method but that the full potential of the approach will not be realized until significant advances have been made in both computing hardware and software.
dc.description.departmentMechanical Engineering, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other13825116
dc.identifier.urihttps://hdl.handle.net/10657/12071
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleNumerical solutions of diffusion-type equations
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Engineering
thesis.degree.departmentMechanical Engineering, Department of
thesis.degree.disciplineMechanical Engineering
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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