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dc.contributor.advisorGomes, Diogo A.
dc.contributor.authorDuisembay, Serikbolsyn
dc.date.accessioned2018-05-07T13:34:34Z
dc.date.available2018-05-07T13:34:34Z
dc.date.issued2018-05-07
dc.identifier.doi10.25781/KAUST-61119
dc.identifier.urihttp://hdl.handle.net/10754/627772
dc.description.abstractIn this thesis, we consider second-order fully nonlinear partial differential equations of elliptic type. Our aim is to develop computational methods using convergent difference schemes for stationary Hamilton-Jacobi equations with Dirichlet and Neumann type boundary conditions in arbitrary two-dimensional domains. First, we introduce the notion of viscosity solutions in both continuous and discontinuous frameworks. Next, we review Barles-Souganidis approach using monotone, consistent, and stable schemes. In particular, we show that these schemes converge locally uniformly to the unique viscosity solution of the first-order Hamilton-Jacobi equations under mild assumptions. To solve the scheme numerically, we use Euler map with some initial guess. This iterative method gives the viscosity solution as a limit. Moreover, we illustrate our numerical approach in several two-dimensional examples.
dc.language.isoen
dc.subjectHamilton-Jacobi equations
dc.subjectdifference schemes
dc.subjectViscosity solutions
dc.subjectnumerical methods
dc.titleConvergent Difference Schemes for Hamilton-Jacobi equations
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberAlouini, Mohamed-Slim
dc.contributor.committeememberParsani, Matteo
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameMaster of Science
refterms.dateFOA2018-06-13T10:56:35Z


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