Publication Date

5-2016

Date of Final Oral Examination (Defense)

3-4-2016

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Supervisory Committee Chair

Barbara Zubik-Kowal, Ph.D.

Supervisory Committee Member

M. Randall Holmes, Ph.D.

Supervisory Committee Member

Uwe Kaiser, Ph.D.

Abstract

While constructive insight for a multitude of phenomena appearing in the physical and biological sciences, medicine, engineering and economics can be gained through the analysis of mathematical models posed in terms of systems of ordinary and partial differential equations, it has been observed that a better description of the behavior of the investigated phenomena can be achieved through the use of functional differential equations (FDEs) or partial functional differential equations (PFDEs). PFDEs or functional equations with ordinary derivatives are subclasses of FDEs. FDEs form a general class of differential equations applied in a variety of disciplines and are characterized by rates of change that depend on the state of the system. As opposed to traditional partial differential equations (PDEs), the formulation of PFDEs, and hence, their methods of solution, are generally significantly complicated by the functional dependence of the system. Consequently, mathematical analysis has become essential to address important questions on PFDEs, their properties and solutions. This thesis is devoted to a general class of parabolic PFDEs and works out the details of the proof techniques of a related paper that help to address these questions. In particular, we examine error bounds of approximate solutions with the aim to address whether or not they converge to the exact solutions as a result of refining the associated discretization.

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