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dc.contributor.advisorSheng, Qin.
dc.creatorPadgett, Josh Lee, 1990-
dc.date.accessioned2017-09-28T12:55:58Z
dc.date.available2017-09-28T12:55:58Z
dc.date.created2017-08
dc.date.issued2017-07-08
dc.date.submittedAugust 2017
dc.identifier.urihttp://hdl.handle.net/2104/10099
dc.description.abstractIn this dissertation, we explore and analyze highly effective and efficient computational procedures for solving a class of nonlinear and stochastic partial differential equations. We are particularly interested in degenerate Kawarada equations arising from numerous multiphysics applications including solid fuel combustion and oil pipeline decay. These differential equations are characterized by their strong degeneracies on the boundary, quenching blow-up singularities in the spatial domain, and vibrant stochastic influences in the evolution processes. In addition, physically relevant numerical solutions to Kawarada-type equations must preserve their positivity and monotonicity in time throughout computations, for all valid initial datum. In light of these concerns and challenges, the numerical methods and analysis developed in this dissertation incorporate nonuniform finite difference approximations of the underlying singular differential equation on arbitrary spatial grids. These approximations are then advanced in time via proper adaptive mechanisms and splitting procedures, when multiple dimensions are involved. Degenerate stochastic Kawarada equations in one-, two-, and three-dimensions are explored. The numerical procedures developed in each case are rigorously shown to not only be unconditionally stable, but also preserve the anticipated solution positivity and monotonicity throughout computations. While the numerical stability is proven in the local linearized sense, the stability analysis has been successfully extended to a novel setting that significantly considers all nonlinear influences. Nonlinear convergence of the quenching numerical solutions, as well as their temporal derivatives, are discussed and assessed through generalized Milne devices for the two-dimensional problem. These explorations offer new insights into the computations of similar singular and stochastic differential equation problems. Intensive simulation experiments and validations are provided.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectPartial differential equations. Operator splitting methods.
dc.titleSolving degenerate stochastic Kawarada partial differential equations via adaptive splitting methods.
dc.typeThesis
dc.rights.accessrightsNo access - Contact librarywebmaster@baylor.edu
dc.type.materialtext
thesis.degree.namePh.D.
thesis.degree.departmentBaylor University. Dept. of Mathematics.
thesis.degree.grantorBaylor University
thesis.degree.levelDoctoral
dc.date.updated2017-09-28T12:55:59Z
local.embargo.lift2019-08-01
local.embargo.terms2019-08-01


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