dc.contributor.advisor Yan, Yubin en_GB dc.contributor.author Atallah, Samia A. * dc.date.accessioned 2012-07-03T15:02:26Z en dc.date.available 2012-07-03T15:02:26Z en dc.date.issued 2011-09 en dc.identifier.uri http://hdl.handle.net/10034/231920 en dc.description.abstract Fractional differential equations, particularly fractional partial differential equations (FPDEs) have many applications in areas such as diffusion processes, electromagnetics, electrochemistry, material science and turbulent flow. There are lots of work for the existence and uniqueness of the solutions for fractional partial differential equations. In recent years, people start to consider the numerical methods for solving fractional partial differential equation. The numerical methods include finite difference method, finite element method and the spectral method. In this dissertation, we mainly consider the finite element method, for the time fractional partial differential equation. We consider both time discretization and space discretization. We obtain the optimal error estimates both in time and space. The numerical examples demonstrate that the numerical results are consistent with the theoretical results. dc.language.iso en en dc.publisher University of Chester en dc.subject fractional partial differential equations en_GB dc.subject finite element method en_GB dc.subject Caputo fractional derivative en_GB dc.subject Riemann-Liouville fractional derivative en_GB dc.title A finite element method for time fractional partial differential equations en_GB dc.type Thesis or dissertation en dc.type.qualificationname MSc en dc.type.qualificationlevel Masters Degree en refterms.dateFOA 2018-08-13T18:21:22Z html.description.abstract Fractional differential equations, particularly fractional partial differential equations (FPDEs) have many applications in areas such as diffusion processes, electromagnetics, electrochemistry, material science and turbulent flow. There are lots of work for the existence and uniqueness of the solutions for fractional partial differential equations. In recent years, people start to consider the numerical methods for solving fractional partial differential equation. The numerical methods include finite difference method, finite element method and the spectral method. In this dissertation, we mainly consider the finite element method, for the time fractional partial differential equation. We consider both time discretization and space discretization. We obtain the optimal error estimates both in time and space. The numerical examples demonstrate that the numerical results are consistent with the theoretical results.
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