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Thesis - University Access Only
Master of Science (MS)
Department / School
Mathematics and Statistics
In this thesis we study the implicit space-time discretization of the one space plus one time dimensional Dirac equation. We show that it is possible to create a stable discrete form of the Dirac initial value problem without modification to the Dirac operator or the addition of artificial stabilizers to our system. This is accomplished by treating space and time simultaneously and by careful choice of function space for the discrete form.Several space time approaches to the Dirac equation are studid, including discretizations based on both finite difference and finite element methods.We find that the use of first order Lagrangian tensor elements produces the most accurate numerical performance and most consistent convergence to the expected solution of the massless,gauge-free Dirac initial value problem.
Library of Congress Subject Headings
Space and time--Mathematics
Includes bibliographical references (pages 47-49).
Number of Pages
South Dakota State University
In Copyright - Educational Use Permitted
Vaselaar, Robert, "Implicit Space-time Discretization of the Dirac Equation" (2013). Electronic Theses and Dissertations. 1633.