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Document Type

Thesis - University Access Only

Award Date


Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Jung-Han Kimu

Second Advisor

Dongming Mei


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

Dirac equation
Space and time--Mathematics


Includes bibliographical references (pages 47-49).



Number of Pages



South Dakota State University


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