dc.contributor.advisor Gomes, Diogo A. dc.contributor.author Duisembay, Serikbolsyn dc.date.accessioned 2018-05-07T13:34:34Z dc.date.available 2018-05-07T13:34:34Z dc.date.issued 2018-05-07 dc.identifier.doi 10.25781/KAUST-61119 dc.identifier.uri http://hdl.handle.net/10754/627772 dc.description.abstract In 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.iso en dc.subject Hamilton-Jacobi equations dc.subject difference schemes dc.subject Viscosity solutions dc.subject numerical methods dc.title Convergent Difference Schemes for Hamilton-Jacobi equations dc.type Thesis dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division thesis.degree.grantor King Abdullah University of Science and Technology dc.contributor.committeemember Alouini, Mohamed-Slim dc.contributor.committeemember Parsani, Matteo thesis.degree.discipline Applied Mathematics and Computational Science thesis.degree.name Master of Science refterms.dateFOA 2018-06-13T10:56:35Z
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